input stringlengths 11 386 | instruction stringclasses 57
values | answer stringlengths 1 84 |
|---|---|---|
-1, 0, 1, 2, 3, 4, 5, 6, __ | To find the next number: Imagine you’re counting up with a special rule. You start with a number called 'a'—that’s your first number. Then, you pick another number called 'd', which is how much you add each time. For example, if a = 2 and d = 3, you begin with 2, then add 3 to get 5, add 3 again to get 8, add 3 again t... | 7 |
-5, -1, 3, 7, 11, 15, __ | To find the next number: Imagine you’re counting up with a special rule. You start with a number called 'a'—that’s your first number. Then, you pick another number called 'd', which is how much you add each time. For example, if a = 2 and d = 3, you begin with 2, then add 3 to get 5, add 3 again to get 8, add 3 again t... | 19 |
6, 8, 10, 12, 14, 16, 18, 20, __ | To find the next number: Imagine you’re counting up with a special rule. You start with a number called 'a'—that’s your first number. Then, you pick another number called 'd', which is how much you add each time. For example, if a = 2 and d = 3, you begin with 2, then add 3 to get 5, add 3 again to get 8, add 3 again t... | 22 |
-6, -3, 0, 3, 6, 9, 12, 15, __ | To find the next number: Imagine you’re counting up with a special rule. You start with a number called 'a'—that’s your first number. Then, you pick another number called 'd', which is how much you add each time. For example, if a = 2 and d = 3, you begin with 2, then add 3 to get 5, add 3 again to get 8, add 3 again t... | 18 |
2, 4, 6, 8, 10, 12, __ | To find the next number: Imagine you’re counting up with a special rule. You start with a number called 'a'—that’s your first number. Then, you pick another number called 'd', which is how much you add each time. For example, if a = 2 and d = 3, you begin with 2, then add 3 to get 5, add 3 again to get 8, add 3 again t... | 14 |
3, 6, 12, 24, 48, 96, 192, 384, __ | To find the next number: Think of this as growing fast with multiplication. You start with a number called 'a'—that’s your first number. Then, you choose a number called 'r', which is what you multiply by each time. For example, if a = 3 and r = 2, you begin with 3, then multiply by 2 to get 6, multiply 6 by 2 to get 1... | 768 |
5, 20, 80, 320, 1280, 5120, __ | To find the next number: Think of this as growing fast with multiplication. You start with a number called 'a'—that’s your first number. Then, you choose a number called 'r', which is what you multiply by each time. For example, if a = 3 and r = 2, you begin with 3, then multiply by 2 to get 6, multiply 6 by 2 to get 1... | 20480 |
5, 15, 45, 135, 405, 1215, 3645, 10935, __ | To find the next number: Think of this as growing fast with multiplication. You start with a number called 'a'—that’s your first number. Then, you choose a number called 'r', which is what you multiply by each time. For example, if a = 3 and r = 2, you begin with 3, then multiply by 2 to get 6, multiply 6 by 2 to get 1... | 32805 |
5, 20, 80, 320, 1280, 5120, 20480, __ | To find the next number: Think of this as growing fast with multiplication. You start with a number called 'a'—that’s your first number. Then, you choose a number called 'r', which is what you multiply by each time. For example, if a = 3 and r = 2, you begin with 3, then multiply by 2 to get 6, multiply 6 by 2 to get 1... | 81920 |
4, 16, 64, 256, 1024, 4096, 16384, 65536, __ | To find the next number: Think of this as growing fast with multiplication. You start with a number called 'a'—that’s your first number. Then, you choose a number called 'r', which is what you multiply by each time. For example, if a = 3 and r = 2, you begin with 3, then multiply by 2 to get 6, multiply 6 by 2 to get 1... | 262144 |
3, -1, -5, -9, -13, -17, -21, __ | To find the next number: Picture yourself counting down with a steady rule. You start with a number called 'a'—that’s where you begin. Then, pick a number called 'd', which is what you subtract each time. For example, if a = 10 and d = 2, you start at 10, subtract 2 to get 8, subtract 2 again to get 6, subtract 2 again... | -25 |
-2, -5, -8, -11, -14, -17, -20, -23, __ | To find the next number: Picture yourself counting down with a steady rule. You start with a number called 'a'—that’s where you begin. Then, pick a number called 'd', which is what you subtract each time. For example, if a = 10 and d = 2, you start at 10, subtract 2 to get 8, subtract 2 again to get 6, subtract 2 again... | -26 |
-5, -9, -13, -17, -21, -25, -29, -33, __ | To find the next number: Picture yourself counting down with a steady rule. You start with a number called 'a'—that’s where you begin. Then, pick a number called 'd', which is what you subtract each time. For example, if a = 10 and d = 2, you start at 10, subtract 2 to get 8, subtract 2 again to get 6, subtract 2 again... | -37 |
2, -2, -6, -10, -14, -18, -22, __ | To find the next number: Picture yourself counting down with a steady rule. You start with a number called 'a'—that’s where you begin. Then, pick a number called 'd', which is what you subtract each time. For example, if a = 10 and d = 2, you start at 10, subtract 2 to get 8, subtract 2 again to get 6, subtract 2 again... | -26 |
-2, -7, -12, -17, -22, -27, -32, __ | To find the next number: Picture yourself counting down with a steady rule. You start with a number called 'a'—that’s where you begin. Then, pick a number called 'd', which is what you subtract each time. For example, if a = 10 and d = 2, you start at 10, subtract 2 to get 8, subtract 2 again to get 6, subtract 2 again... | -37 |
1, 2, 6, 24, 120, 720, 5040, __ | To find the next number: This sequence is all about multiplying numbers together, and it gets big fast! Each term is the result of multiplying all the numbers from 1 up to its position, starting with position 1. For example, it goes 1 (just 1), 2 (2 × 1), 6 (3 × 2 × 1), 24 (4 × 3 × 2 × 1). Here’s how to do it: Look at ... | 40320 |
1, 2, 6, 24, 120, 720, 5040, __ | To find the next number: This sequence is all about multiplying numbers together, and it gets big fast! Each term is the result of multiplying all the numbers from 1 up to its position, starting with position 1. For example, it goes 1 (just 1), 2 (2 × 1), 6 (3 × 2 × 1), 24 (4 × 3 × 2 × 1). Here’s how to do it: Look at ... | 40320 |
1, 2, 6, 24, 120, 720, 5040, __ | To find the next number: This sequence is all about multiplying numbers together, and it gets big fast! Each term is the result of multiplying all the numbers from 1 up to its position, starting with position 1. For example, it goes 1 (just 1), 2 (2 × 1), 6 (3 × 2 × 1), 24 (4 × 3 × 2 × 1). Here’s how to do it: Look at ... | 40320 |
1, 2, 6, 24, 120, 720, 5040, __ | To find the next number: This sequence is all about multiplying numbers together, and it gets big fast! Each term is the result of multiplying all the numbers from 1 up to its position, starting with position 1. For example, it goes 1 (just 1), 2 (2 × 1), 6 (3 × 2 × 1), 24 (4 × 3 × 2 × 1). Here’s how to do it: Look at ... | 40320 |
1, 2, 6, 24, 120, 720, 5040, __ | To find the next number: This sequence is all about multiplying numbers together, and it gets big fast! Each term is the result of multiplying all the numbers from 1 up to its position, starting with position 1. For example, it goes 1 (just 1), 2 (2 × 1), 6 (3 × 2 × 1), 24 (4 × 3 × 2 × 1). Here’s how to do it: Look at ... | 40320 |
0, 1, 1, 2, 3, 5, 8, 13, __ | To find the next number: This sequence is like a fun game of adding pairs. You start with two numbers: 0 and 1. Then, every number after that is the sum of the two numbers before it. Let’s see: it begins 0, 1, then 0 + 1 = 1, then 1 + 1 = 2, then 1 + 2 = 3, then 2 + 3 = 5, then 3 + 5 = 8. So, the sequence is 0, 1, 1, 2... | 21 |
0, 1, 1, 2, 3, 5, __ | To find the next number: This sequence is like a fun game of adding pairs. You start with two numbers: 0 and 1. Then, every number after that is the sum of the two numbers before it. Let’s see: it begins 0, 1, then 0 + 1 = 1, then 1 + 1 = 2, then 1 + 2 = 3, then 2 + 3 = 5, then 3 + 5 = 8. So, the sequence is 0, 1, 1, 2... | 8 |
0, 1, 1, 2, 3, 5, 8, 13, __ | To find the next number: This sequence is like a fun game of adding pairs. You start with two numbers: 0 and 1. Then, every number after that is the sum of the two numbers before it. Let’s see: it begins 0, 1, then 0 + 1 = 1, then 1 + 1 = 2, then 1 + 2 = 3, then 2 + 3 = 5, then 3 + 5 = 8. So, the sequence is 0, 1, 1, 2... | 21 |
0, 1, 1, 2, 3, 5, __ | To find the next number: This sequence is like a fun game of adding pairs. You start with two numbers: 0 and 1. Then, every number after that is the sum of the two numbers before it. Let’s see: it begins 0, 1, then 0 + 1 = 1, then 1 + 1 = 2, then 1 + 2 = 3, then 2 + 3 = 5, then 3 + 5 = 8. So, the sequence is 0, 1, 1, 2... | 8 |
0, 1, 1, 2, 3, 5, 8, __ | To find the next number: This sequence is like a fun game of adding pairs. You start with two numbers: 0 and 1. Then, every number after that is the sum of the two numbers before it. Let’s see: it begins 0, 1, then 0 + 1 = 1, then 1 + 1 = 2, then 1 + 2 = 3, then 2 + 3 = 5, then 3 + 5 = 8. So, the sequence is 0, 1, 1, 2... | 13 |
2, 1, 3, 4, 7, 11, __ | To find the next number: This is a lot like Fibonacci, but we start with different numbers: 2 and 1. After that, each number is the sum of the two numbers before it. Let’s walk through it: start with 2, 1, then 2 + 1 = 3, then 1 + 3 = 4, then 3 + 4 = 7, then 4 + 7 = 11. The sequence is 2, 1, 3, 4, 7, 11. To find the ne... | 18 |
2, 1, 3, 4, 7, 11, __ | To find the next number: This is a lot like Fibonacci, but we start with different numbers: 2 and 1. After that, each number is the sum of the two numbers before it. Let’s walk through it: start with 2, 1, then 2 + 1 = 3, then 1 + 3 = 4, then 3 + 4 = 7, then 4 + 7 = 11. The sequence is 2, 1, 3, 4, 7, 11. To find the ne... | 18 |
2, 1, 3, 4, 7, 11, 18, 29, __ | To find the next number: This is a lot like Fibonacci, but we start with different numbers: 2 and 1. After that, each number is the sum of the two numbers before it. Let’s walk through it: start with 2, 1, then 2 + 1 = 3, then 1 + 3 = 4, then 3 + 4 = 7, then 4 + 7 = 11. The sequence is 2, 1, 3, 4, 7, 11. To find the ne... | 47 |
2, 1, 3, 4, 7, 11, 18, 29, __ | To find the next number: This is a lot like Fibonacci, but we start with different numbers: 2 and 1. After that, each number is the sum of the two numbers before it. Let’s walk through it: start with 2, 1, then 2 + 1 = 3, then 1 + 3 = 4, then 3 + 4 = 7, then 4 + 7 = 11. The sequence is 2, 1, 3, 4, 7, 11. To find the ne... | 47 |
2, 1, 3, 4, 7, 11, 18, 29, __ | To find the next number: This is a lot like Fibonacci, but we start with different numbers: 2 and 1. After that, each number is the sum of the two numbers before it. Let’s walk through it: start with 2, 1, then 2 + 1 = 3, then 1 + 3 = 4, then 3 + 4 = 7, then 4 + 7 = 11. The sequence is 2, 1, 3, 4, 7, 11. To find the ne... | 47 |
1, 3, 6, 10, 15, 21, 28, 36, __ | To find the next number: Imagine stacking blocks in a triangle, adding one more row each time. Each term is the total number of blocks you’d have if you added all numbers from 1 up to its position, starting at position 1. For example, it’s 1 (just 1), 3 (1 + 2), 6 (1 + 2 + 3), 10 (1 + 2 + 3 + 4). Here’s the trick: Coun... | 45 |
1, 3, 6, 10, 15, 21, __ | To find the next number: Imagine stacking blocks in a triangle, adding one more row each time. Each term is the total number of blocks you’d have if you added all numbers from 1 up to its position, starting at position 1. For example, it’s 1 (just 1), 3 (1 + 2), 6 (1 + 2 + 3), 10 (1 + 2 + 3 + 4). Here’s the trick: Coun... | 28 |
1, 3, 6, 10, 15, 21, 28, __ | To find the next number: Imagine stacking blocks in a triangle, adding one more row each time. Each term is the total number of blocks you’d have if you added all numbers from 1 up to its position, starting at position 1. For example, it’s 1 (just 1), 3 (1 + 2), 6 (1 + 2 + 3), 10 (1 + 2 + 3 + 4). Here’s the trick: Coun... | 36 |
1, 3, 6, 10, 15, 21, __ | To find the next number: Imagine stacking blocks in a triangle, adding one more row each time. Each term is the total number of blocks you’d have if you added all numbers from 1 up to its position, starting at position 1. For example, it’s 1 (just 1), 3 (1 + 2), 6 (1 + 2 + 3), 10 (1 + 2 + 3 + 4). Here’s the trick: Coun... | 28 |
1, 3, 6, 10, 15, 21, 28, __ | To find the next number: Imagine stacking blocks in a triangle, adding one more row each time. Each term is the total number of blocks you’d have if you added all numbers from 1 up to its position, starting at position 1. For example, it’s 1 (just 1), 3 (1 + 2), 6 (1 + 2 + 3), 10 (1 + 2 + 3 + 4). Here’s the trick: Coun... | 36 |
1, 4, 9, 16, 25, 36, 49, __ | To find the next number: This sequence is super simple—it’s just numbers multiplied by themselves! Each term is its position number squared, starting at position 1. For example, it’s 1 (1 × 1), 4 (2 × 2), 9 (3 × 3), 16 (4 × 4). To find the next one, count how many terms you have. Say your list is 1, 4, 9, 16—that’s 4 t... | 64 |
1, 4, 9, 16, 25, 36, 49, 64, __ | To find the next number: This sequence is super simple—it’s just numbers multiplied by themselves! Each term is its position number squared, starting at position 1. For example, it’s 1 (1 × 1), 4 (2 × 2), 9 (3 × 3), 16 (4 × 4). To find the next one, count how many terms you have. Say your list is 1, 4, 9, 16—that’s 4 t... | 81 |
1, 4, 9, 16, 25, 36, 49, 64, __ | To find the next number: This sequence is super simple—it’s just numbers multiplied by themselves! Each term is its position number squared, starting at position 1. For example, it’s 1 (1 × 1), 4 (2 × 2), 9 (3 × 3), 16 (4 × 4). To find the next one, count how many terms you have. Say your list is 1, 4, 9, 16—that’s 4 t... | 81 |
1, 4, 9, 16, 25, 36, 49, 64, __ | To find the next number: This sequence is super simple—it’s just numbers multiplied by themselves! Each term is its position number squared, starting at position 1. For example, it’s 1 (1 × 1), 4 (2 × 2), 9 (3 × 3), 16 (4 × 4). To find the next one, count how many terms you have. Say your list is 1, 4, 9, 16—that’s 4 t... | 81 |
1, 4, 9, 16, 25, 36, __ | To find the next number: This sequence is super simple—it’s just numbers multiplied by themselves! Each term is its position number squared, starting at position 1. For example, it’s 1 (1 × 1), 4 (2 × 2), 9 (3 × 3), 16 (4 × 4). To find the next one, count how many terms you have. Say your list is 1, 4, 9, 16—that’s 4 t... | 49 |
1, 8, 27, 64, 125, 216, 343, 512, __ | To find the next number: This is like stacking cubes—each term is its position number multiplied by itself three times, starting at position 1. For example, it’s 1 (1 × 1 × 1), 8 (2 × 2 × 2), 27 (3 × 3 × 3), 64 (4 × 4 × 4). Here’s how: Count the terms in your list. Say it’s 1, 8, 27, 64—that’s 4 terms. The next positio... | 729 |
1, 8, 27, 64, 125, 216, 343, 512, __ | To find the next number: This is like stacking cubes—each term is its position number multiplied by itself three times, starting at position 1. For example, it’s 1 (1 × 1 × 1), 8 (2 × 2 × 2), 27 (3 × 3 × 3), 64 (4 × 4 × 4). Here’s how: Count the terms in your list. Say it’s 1, 8, 27, 64—that’s 4 terms. The next positio... | 729 |
1, 8, 27, 64, 125, 216, 343, __ | To find the next number: This is like stacking cubes—each term is its position number multiplied by itself three times, starting at position 1. For example, it’s 1 (1 × 1 × 1), 8 (2 × 2 × 2), 27 (3 × 3 × 3), 64 (4 × 4 × 4). Here’s how: Count the terms in your list. Say it’s 1, 8, 27, 64—that’s 4 terms. The next positio... | 512 |
1, 8, 27, 64, 125, 216, 343, 512, __ | To find the next number: This is like stacking cubes—each term is its position number multiplied by itself three times, starting at position 1. For example, it’s 1 (1 × 1 × 1), 8 (2 × 2 × 2), 27 (3 × 3 × 3), 64 (4 × 4 × 4). Here’s how: Count the terms in your list. Say it’s 1, 8, 27, 64—that’s 4 terms. The next positio... | 729 |
1, 8, 27, 64, 125, 216, 343, __ | To find the next number: This is like stacking cubes—each term is its position number multiplied by itself three times, starting at position 1. For example, it’s 1 (1 × 1 × 1), 8 (2 × 2 × 2), 27 (3 × 3 × 3), 64 (4 × 4 × 4). Here’s how: Count the terms in your list. Say it’s 1, 8, 27, 64—that’s 4 terms. The next positio... | 512 |
1.0, 0.5, 0.33, 0.25, 0.2, 0.17, 0.14, __ | To find the next number: This sequence is about dividing 1 by bigger and bigger numbers, starting at position 1. Each term is 1 divided by its position, rounded to 2 decimal places for simplicity. For example, it’s 1.00 (1 ÷ 1), 0.50 (1 ÷ 2), 0.33 (1 ÷ 3), 0.25 (1 ÷ 4). To find the next one, count your terms. Say it’s ... | 0.12 |
1.0, 0.5, 0.33, 0.25, 0.2, 0.17, 0.14, __ | To find the next number: This sequence is about dividing 1 by bigger and bigger numbers, starting at position 1. Each term is 1 divided by its position, rounded to 2 decimal places for simplicity. For example, it’s 1.00 (1 ÷ 1), 0.50 (1 ÷ 2), 0.33 (1 ÷ 3), 0.25 (1 ÷ 4). To find the next one, count your terms. Say it’s ... | 0.12 |
1.0, 0.5, 0.33, 0.25, 0.2, 0.17, 0.14, 0.12, __ | To find the next number: This sequence is about dividing 1 by bigger and bigger numbers, starting at position 1. Each term is 1 divided by its position, rounded to 2 decimal places for simplicity. For example, it’s 1.00 (1 ÷ 1), 0.50 (1 ÷ 2), 0.33 (1 ÷ 3), 0.25 (1 ÷ 4). To find the next one, count your terms. Say it’s ... | 0.11 |
1.0, 0.5, 0.33, 0.25, 0.2, 0.17, 0.14, __ | To find the next number: This sequence is about dividing 1 by bigger and bigger numbers, starting at position 1. Each term is 1 divided by its position, rounded to 2 decimal places for simplicity. For example, it’s 1.00 (1 ÷ 1), 0.50 (1 ÷ 2), 0.33 (1 ÷ 3), 0.25 (1 ÷ 4). To find the next one, count your terms. Say it’s ... | 0.12 |
1.0, 0.5, 0.33, 0.25, 0.2, 0.17, 0.14, __ | To find the next number: This sequence is about dividing 1 by bigger and bigger numbers, starting at position 1. Each term is 1 divided by its position, rounded to 2 decimal places for simplicity. For example, it’s 1.00 (1 ÷ 1), 0.50 (1 ÷ 2), 0.33 (1 ÷ 3), 0.25 (1 ÷ 4). To find the next one, count your terms. Say it’s ... | 0.12 |
1, 4, 16, 64, 256, 1024, 4096, 16384, __ | To find the next number: This is like a number growing taller each step! You pick a base number called 'b', and each term is b raised to a bigger power, starting at position 0 (where the power is 0). For example, if b = 2, it’s 1 (2^0), 2 (2^1), 4 (2^2), 8 (2^3). Count your terms. Say it’s 1, 2, 4, 8—that’s 4 terms (po... | 65536 |
1, 3, 9, 27, 81, 243, 729, 2187, __ | To find the next number: This is like a number growing taller each step! You pick a base number called 'b', and each term is b raised to a bigger power, starting at position 0 (where the power is 0). For example, if b = 2, it’s 1 (2^0), 2 (2^1), 4 (2^2), 8 (2^3). Count your terms. Say it’s 1, 2, 4, 8—that’s 4 terms (po... | 6561 |
1, 3, 9, 27, 81, 243, __ | To find the next number: This is like a number growing taller each step! You pick a base number called 'b', and each term is b raised to a bigger power, starting at position 0 (where the power is 0). For example, if b = 2, it’s 1 (2^0), 2 (2^1), 4 (2^2), 8 (2^3). Count your terms. Say it’s 1, 2, 4, 8—that’s 4 terms (po... | 729 |
1, 4, 16, 64, 256, 1024, __ | To find the next number: This is like a number growing taller each step! You pick a base number called 'b', and each term is b raised to a bigger power, starting at position 0 (where the power is 0). For example, if b = 2, it’s 1 (2^0), 2 (2^1), 4 (2^2), 8 (2^3). Count your terms. Say it’s 1, 2, 4, 8—that’s 4 terms (po... | 4096 |
1, 3, 9, 27, 81, 243, 729, 2187, __ | To find the next number: This is like a number growing taller each step! You pick a base number called 'b', and each term is b raised to a bigger power, starting at position 0 (where the power is 0). For example, if b = 2, it’s 1 (2^0), 2 (2^1), 4 (2^2), 8 (2^3). Count your terms. Say it’s 1, 2, 4, 8—that’s 4 terms (po... | 6561 |
1, 1, 2, 5, 14, 42, 132, __ | To find the next number: This sequence counts special patterns, like ways to match pairs, and it uses a big multiplication rule called Catalan numbers. It starts at position 0 with 1, then 1, 2, 5, 14. The rule is: multiply all numbers up to 2 times the position, then divide by (position + 1) times all numbers up to th... | 429 |
1, 1, 2, 5, 14, 42, __ | To find the next number: This sequence counts special patterns, like ways to match pairs, and it uses a big multiplication rule called Catalan numbers. It starts at position 0 with 1, then 1, 2, 5, 14. The rule is: multiply all numbers up to 2 times the position, then divide by (position + 1) times all numbers up to th... | 132 |
1, 1, 2, 5, 14, 42, 132, __ | To find the next number: This sequence counts special patterns, like ways to match pairs, and it uses a big multiplication rule called Catalan numbers. It starts at position 0 with 1, then 1, 2, 5, 14. The rule is: multiply all numbers up to 2 times the position, then divide by (position + 1) times all numbers up to th... | 429 |
1, 1, 2, 5, 14, 42, __ | To find the next number: This sequence counts special patterns, like ways to match pairs, and it uses a big multiplication rule called Catalan numbers. It starts at position 0 with 1, then 1, 2, 5, 14. The rule is: multiply all numbers up to 2 times the position, then divide by (position + 1) times all numbers up to th... | 132 |
1, 1, 2, 5, 14, 42, 132, __ | To find the next number: This sequence counts special patterns, like ways to match pairs, and it uses a big multiplication rule called Catalan numbers. It starts at position 0 with 1, then 1, 2, 5, 14. The rule is: multiply all numbers up to 2 times the position, then divide by (position + 1) times all numbers up to th... | 429 |
2, 3, 5, 7, 11, 13, __ | To find the next number: This sequence is all about special numbers called primes—they’re only divisible by 1 and themselves, like 2, 3, 5, 7, 11, 13, 17, 19. To find the next one, look at your list. Say it’s 2, 3, 5, 7, 11, 13—that’s 6 terms. The last number is 13. Now, check numbers after 13 to find the next prime: 1... | 17 |
2, 3, 5, 7, 11, 13, 17, __ | To find the next number: This sequence is all about special numbers called primes—they’re only divisible by 1 and themselves, like 2, 3, 5, 7, 11, 13, 17, 19. To find the next one, look at your list. Say it’s 2, 3, 5, 7, 11, 13—that’s 6 terms. The last number is 13. Now, check numbers after 13 to find the next prime: 1... | 19 |
2, 3, 5, 7, 11, 13, 17, __ | To find the next number: This sequence is all about special numbers called primes—they’re only divisible by 1 and themselves, like 2, 3, 5, 7, 11, 13, 17, 19. To find the next one, look at your list. Say it’s 2, 3, 5, 7, 11, 13—that’s 6 terms. The last number is 13. Now, check numbers after 13 to find the next prime: 1... | 19 |
2, 3, 5, 7, 11, 13, 17, __ | To find the next number: This sequence is all about special numbers called primes—they’re only divisible by 1 and themselves, like 2, 3, 5, 7, 11, 13, 17, 19. To find the next one, look at your list. Say it’s 2, 3, 5, 7, 11, 13—that’s 6 terms. The last number is 13. Now, check numbers after 13 to find the next prime: 1... | 19 |
2, 3, 5, 7, 11, 13, 17, 19, __ | To find the next number: This sequence is all about special numbers called primes—they’re only divisible by 1 and themselves, like 2, 3, 5, 7, 11, 13, 17, 19. To find the next one, look at your list. Say it’s 2, 3, 5, 7, 11, 13—that’s 6 terms. The last number is 13. Now, check numbers after 13 to find the next prime: 1... | 19 |
1, 4, 10, 20, 35, 56, 84, __ | To find the next number: Imagine stacking balls in a pyramid with a triangular base—that’s what this sequence does! Each term is the total balls if you stack layers up to its position, starting at 1. The formula is position × (position + 1) × (position + 2) ÷ 6. For example: 1 (1st), 4 (2nd), 10 (3rd), 20 (4th). Count ... | 120 |
1, 4, 10, 20, 35, 56, 84, __ | To find the next number: Imagine stacking balls in a pyramid with a triangular base—that’s what this sequence does! Each term is the total balls if you stack layers up to its position, starting at 1. The formula is position × (position + 1) × (position + 2) ÷ 6. For example: 1 (1st), 4 (2nd), 10 (3rd), 20 (4th). Count ... | 120 |
1, 4, 10, 20, 35, 56, __ | To find the next number: Imagine stacking balls in a pyramid with a triangular base—that’s what this sequence does! Each term is the total balls if you stack layers up to its position, starting at 1. The formula is position × (position + 1) × (position + 2) ÷ 6. For example: 1 (1st), 4 (2nd), 10 (3rd), 20 (4th). Count ... | 84 |
1, 4, 10, 20, 35, 56, 84, __ | To find the next number: Imagine stacking balls in a pyramid with a triangular base—that’s what this sequence does! Each term is the total balls if you stack layers up to its position, starting at 1. The formula is position × (position + 1) × (position + 2) ÷ 6. For example: 1 (1st), 4 (2nd), 10 (3rd), 20 (4th). Count ... | 120 |
1, 4, 10, 20, 35, 56, 84, 120, __ | To find the next number: Imagine stacking balls in a pyramid with a triangular base—that’s what this sequence does! Each term is the total balls if you stack layers up to its position, starting at 1. The formula is position × (position + 1) × (position + 2) ÷ 6. For example: 1 (1st), 4 (2nd), 10 (3rd), 20 (4th). Count ... | 165 |
1, 5, 12, 22, 35, 51, 70, 92, __ | To find the next number: This sequence makes numbers shaped like a five-sided star! Each term uses the formula position × (3 × position - 1) ÷ 2, starting at position 1. For example: 1 (1 × (3-1) ÷ 2 = 1), 5 (2 × (6-1) ÷ 2 = 5), 12 (3 × (9-1) ÷ 2 = 12), 22 (4 × (12-1) ÷ 2 = 22). Count your terms. Say it’s 1, 5, 12, 22—... | 117 |
1, 5, 12, 22, 35, 51, 70, __ | To find the next number: This sequence makes numbers shaped like a five-sided star! Each term uses the formula position × (3 × position - 1) ÷ 2, starting at position 1. For example: 1 (1 × (3-1) ÷ 2 = 1), 5 (2 × (6-1) ÷ 2 = 5), 12 (3 × (9-1) ÷ 2 = 12), 22 (4 × (12-1) ÷ 2 = 22). Count your terms. Say it’s 1, 5, 12, 22—... | 92 |
1, 5, 12, 22, 35, 51, 70, __ | To find the next number: This sequence makes numbers shaped like a five-sided star! Each term uses the formula position × (3 × position - 1) ÷ 2, starting at position 1. For example: 1 (1 × (3-1) ÷ 2 = 1), 5 (2 × (6-1) ÷ 2 = 5), 12 (3 × (9-1) ÷ 2 = 12), 22 (4 × (12-1) ÷ 2 = 22). Count your terms. Say it’s 1, 5, 12, 22—... | 92 |
1, 5, 12, 22, 35, 51, __ | To find the next number: This sequence makes numbers shaped like a five-sided star! Each term uses the formula position × (3 × position - 1) ÷ 2, starting at position 1. For example: 1 (1 × (3-1) ÷ 2 = 1), 5 (2 × (6-1) ÷ 2 = 5), 12 (3 × (9-1) ÷ 2 = 12), 22 (4 × (12-1) ÷ 2 = 22). Count your terms. Say it’s 1, 5, 12, 22—... | 70 |
1, 5, 12, 22, 35, 51, 70, __ | To find the next number: This sequence makes numbers shaped like a five-sided star! Each term uses the formula position × (3 × position - 1) ÷ 2, starting at position 1. For example: 1 (1 × (3-1) ÷ 2 = 1), 5 (2 × (6-1) ÷ 2 = 5), 12 (3 × (9-1) ÷ 2 = 12), 22 (4 × (12-1) ÷ 2 = 22). Count your terms. Say it’s 1, 5, 12, 22—... | 92 |
1, 0, -1, 0, 5, 0, __ | To find the next number: This sequence is a special list used in math, called Euler numbers, and it doesn’t follow an easy formula—it’s fixed: 1, 0, -1, 0, 5, 0, -61, 0, and so on, with zeros every other term. To find the next one, count your terms. Say it’s 1, 0, -1, 0, 5—that’s 5 terms (positions 1 to 5). The next is... | 0 |
1, 0, -1, 0, 5, 0, __ | To find the next number: This sequence is a special list used in math, called Euler numbers, and it doesn’t follow an easy formula—it’s fixed: 1, 0, -1, 0, 5, 0, -61, 0, and so on, with zeros every other term. To find the next one, count your terms. Say it’s 1, 0, -1, 0, 5—that’s 5 terms (positions 1 to 5). The next is... | 0 |
1, 0, -1, 0, 5, 0, __ | To find the next number: This sequence is a special list used in math, called Euler numbers, and it doesn’t follow an easy formula—it’s fixed: 1, 0, -1, 0, 5, 0, -61, 0, and so on, with zeros every other term. To find the next one, count your terms. Say it’s 1, 0, -1, 0, 5—that’s 5 terms (positions 1 to 5). The next is... | 0 |
1, 0, -1, 0, 5, 0, __ | To find the next number: This sequence is a special list used in math, called Euler numbers, and it doesn’t follow an easy formula—it’s fixed: 1, 0, -1, 0, 5, 0, -61, 0, and so on, with zeros every other term. To find the next one, count your terms. Say it’s 1, 0, -1, 0, 5—that’s 5 terms (positions 1 to 5). The next is... | 0 |
1, 0, -1, 0, 5, 0, __ | To find the next number: This sequence is a special list used in math, called Euler numbers, and it doesn’t follow an easy formula—it’s fixed: 1, 0, -1, 0, 5, 0, -61, 0, and so on, with zeros every other term. To find the next one, count your terms. Say it’s 1, 0, -1, 0, 5—that’s 5 terms (positions 1 to 5). The next is... | 0 |
1, -0.5, 0.1667, 0, -0.0333, __ | To find the next number: This is another math list called Bernoulli numbers, and it’s fixed: 1, -0.5, 0.1667, 0, -0.0333, 0, and so on, with lots of zeros later. To find the next one, count your terms. Say it’s 1, -0.5, 0.1667, 0, -0.0333—that’s 5 terms (positions 1 to 5). Next is position 6, which is 0 (most terms aft... | -0.0333 |
1, -0.5, 0.1667, 0, -0.0333, __ | To find the next number: This is another math list called Bernoulli numbers, and it’s fixed: 1, -0.5, 0.1667, 0, -0.0333, 0, and so on, with lots of zeros later. To find the next one, count your terms. Say it’s 1, -0.5, 0.1667, 0, -0.0333—that’s 5 terms (positions 1 to 5). Next is position 6, which is 0 (most terms aft... | -0.0333 |
1, -0.5, 0.1667, 0, -0.0333, __ | To find the next number: This is another math list called Bernoulli numbers, and it’s fixed: 1, -0.5, 0.1667, 0, -0.0333, 0, and so on, with lots of zeros later. To find the next one, count your terms. Say it’s 1, -0.5, 0.1667, 0, -0.0333—that’s 5 terms (positions 1 to 5). Next is position 6, which is 0 (most terms aft... | -0.0333 |
1, -0.5, 0.1667, 0, -0.0333, __ | To find the next number: This is another math list called Bernoulli numbers, and it’s fixed: 1, -0.5, 0.1667, 0, -0.0333, 0, and so on, with lots of zeros later. To find the next one, count your terms. Say it’s 1, -0.5, 0.1667, 0, -0.0333—that’s 5 terms (positions 1 to 5). Next is position 6, which is 0 (most terms aft... | -0.0333 |
1, -0.5, 0.1667, 0, -0.0333, __ | To find the next number: This is another math list called Bernoulli numbers, and it’s fixed: 1, -0.5, 0.1667, 0, -0.0333, 0, and so on, with lots of zeros later. To find the next one, count your terms. Say it’s 1, -0.5, 0.1667, 0, -0.0333—that’s 5 terms (positions 1 to 5). Next is position 6, which is 0 (most terms aft... | -0.0333 |
1, 3, 11, 50, 274, 1764, 13068, __ | To find the next number: This sequence counts ways to arrange items in circles, using Stirling numbers of the first kind for 2 circles, starting at position 2: 1, 2, 6, 24, 120. Each term grows fast! Count your terms. Say it’s 1, 2, 6, 24—that’s 4 terms (positions 2 to 5). Next is position 6: multiply all numbers up to... | 109584 |
1, 3, 11, 50, 274, 1764, 13068, __ | To find the next number: This sequence counts ways to arrange items in circles, using Stirling numbers of the first kind for 2 circles, starting at position 2: 1, 2, 6, 24, 120. Each term grows fast! Count your terms. Say it’s 1, 2, 6, 24—that’s 4 terms (positions 2 to 5). Next is position 6: multiply all numbers up to... | 109584 |
1, 3, 11, 50, 274, 1764, __ | To find the next number: This sequence counts ways to arrange items in circles, using Stirling numbers of the first kind for 2 circles, starting at position 2: 1, 2, 6, 24, 120. Each term grows fast! Count your terms. Say it’s 1, 2, 6, 24—that’s 4 terms (positions 2 to 5). Next is position 6: multiply all numbers up to... | 13068 |
1, 3, 11, 50, 274, 1764, 13068, __ | To find the next number: This sequence counts ways to arrange items in circles, using Stirling numbers of the first kind for 2 circles, starting at position 2: 1, 2, 6, 24, 120. Each term grows fast! Count your terms. Say it’s 1, 2, 6, 24—that’s 4 terms (positions 2 to 5). Next is position 6: multiply all numbers up to... | 109584 |
1, 3, 11, 50, 274, 1764, __ | To find the next number: This sequence counts ways to arrange items in circles, using Stirling numbers of the first kind for 2 circles, starting at position 2: 1, 2, 6, 24, 120. Each term grows fast! Count your terms. Say it’s 1, 2, 6, 24—that’s 4 terms (positions 2 to 5). Next is position 6: multiply all numbers up to... | 13068 |
1, 3, 7, 15, 31, 63, __ | To find the next number: This counts ways to split items into 2 groups, using Stirling numbers of the second kind, starting at position 2: 1, 3, 7, 15, 31. Count your terms. Say it’s 1, 3, 7, 15—that’s 4 terms (positions 2 to 5). Next is position 6: use the rule 2^(position-1) - 1 = 2^5 - 1 = 32 - 1 = 31. That’s your a... | 127 |
1, 3, 7, 15, 31, 63, __ | To find the next number: This counts ways to split items into 2 groups, using Stirling numbers of the second kind, starting at position 2: 1, 3, 7, 15, 31. Count your terms. Say it’s 1, 3, 7, 15—that’s 4 terms (positions 2 to 5). Next is position 6: use the rule 2^(position-1) - 1 = 2^5 - 1 = 32 - 1 = 31. That’s your a... | 127 |
1, 3, 7, 15, 31, 63, 127, __ | To find the next number: This counts ways to split items into 2 groups, using Stirling numbers of the second kind, starting at position 2: 1, 3, 7, 15, 31. Count your terms. Say it’s 1, 3, 7, 15—that’s 4 terms (positions 2 to 5). Next is position 6: use the rule 2^(position-1) - 1 = 2^5 - 1 = 32 - 1 = 31. That’s your a... | 255 |
1, 3, 7, 15, 31, 63, 127, 255, __ | To find the next number: This counts ways to split items into 2 groups, using Stirling numbers of the second kind, starting at position 2: 1, 3, 7, 15, 31. Count your terms. Say it’s 1, 3, 7, 15—that’s 4 terms (positions 2 to 5). Next is position 6: use the rule 2^(position-1) - 1 = 2^5 - 1 = 32 - 1 = 31. That’s your a... | 511 |
1, 3, 7, 15, 31, 63, __ | To find the next number: This counts ways to split items into 2 groups, using Stirling numbers of the second kind, starting at position 2: 1, 3, 7, 15, 31. Count your terms. Say it’s 1, 3, 7, 15—that’s 4 terms (positions 2 to 5). Next is position 6: use the rule 2^(position-1) - 1 = 2^5 - 1 = 32 - 1 = 31. That’s your a... | 127 |
1, 2, 5, 15, 52, 203, __ | To find the next number: This sequence, called Bell numbers, counts all possible ways to group items, starting at position 1: 1, 2, 5, 15, 52. Count your terms. Say it’s 1, 2, 5, 15—that’s 4 terms (positions 1 to 4). Next is 5th: add up ways to split 5 items into groups (1 + 10 + 25 + 10 + 1 = 52 from a table or rule).... | 877 |
1, 2, 5, 15, 52, 203, __ | To find the next number: This sequence, called Bell numbers, counts all possible ways to group items, starting at position 1: 1, 2, 5, 15, 52. Count your terms. Say it’s 1, 2, 5, 15—that’s 4 terms (positions 1 to 4). Next is 5th: add up ways to split 5 items into groups (1 + 10 + 25 + 10 + 1 = 52 from a table or rule).... | 877 |
1, 2, 5, 15, 52, 203, 877, 4140, __ | To find the next number: This sequence, called Bell numbers, counts all possible ways to group items, starting at position 1: 1, 2, 5, 15, 52. Count your terms. Say it’s 1, 2, 5, 15—that’s 4 terms (positions 1 to 4). Next is 5th: add up ways to split 5 items into groups (1 + 10 + 25 + 10 + 1 = 52 from a table or rule).... | 21147 |
1, 2, 5, 15, 52, 203, __ | To find the next number: This sequence, called Bell numbers, counts all possible ways to group items, starting at position 1: 1, 2, 5, 15, 52. Count your terms. Say it’s 1, 2, 5, 15—that’s 4 terms (positions 1 to 4). Next is 5th: add up ways to split 5 items into groups (1 + 10 + 25 + 10 + 1 = 52 from a table or rule).... | 877 |
1, 2, 5, 15, 52, 203, __ | To find the next number: This sequence, called Bell numbers, counts all possible ways to group items, starting at position 1: 1, 2, 5, 15, 52. Count your terms. Say it’s 1, 2, 5, 15—that’s 4 terms (positions 1 to 4). Next is 5th: add up ways to split 5 items into groups (1 + 10 + 25 + 10 + 1 = 52 from a table or rule).... | 877 |
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