Finding the Next Value in a Sequence

Skipping every other day, the next term must be "Wednesday the 2nd", or "W2" (or maybe "W02").
*Find the next number in the sequence:  6, 6, 7, 9, ..."Sunday" is spelled with six letters.
"Monday" is spelled with six letters.
"Tuesday" is spelled with seven letters.
"Wednesday" is spelled with nine letters.
*Find the next term in the sequence:
F21, S23, T25, T27, S29, M31.F21: Friday the 21st.
S23: Sunday the 23rd.
T25: Tuesday the 25th.
T27: Thursday the 27th.
S29: Saturday the 29th.
M31: Monday the 31st.
(If you're not sure about this, then pull out a calendar and find a month where Friday falls on the twenty-first. See where this leads you.)
*Find the missing term in the seqence:  325, 446, 567, ___, 709, 820.
Consider the digits for the units, tens, and hundreds places separately:
They're adding by one in the hundreds and ones digits, and adding by twos in the tens digit.
*hundreds digits: 3, 4, 5, ___, 7, 8 
tens digits: 2, 4, 6, ___, 0, 2 
ones digits: 5, 6, 7, ___, 9, 0 
The missing term is 688.
*Find the missing term in the sequence: 127863, 12789, ____, 135, 18
Look at the last two digits of the given numbers.
Do you see?  They're taking the last two digits, adding them, replacing the last two digits with one zero, and then adding the sum they just found. Completing the pattern:
*127863:  6 + 3 = 9
12789: 8 + 9 = 17
_______
135: 3 + 5 = 8
127863:  6 + 3 = 9:   12780 + 9 = 12789
12789:  8 + 9 = 17:   1270 + 17 = 1287
1287:  8 + 7 = 15:  120 + 15 = 135
135:  3 + 5 = 8:  10 + 8 = 18
The missing number is 1287.
*Given that 1 and 2 yield 9, 3 and 4 yield 20, and 5 and 6 yield 12, find the number after 17 and 12.   Copyright © Elizabeth Stapel 2002-2011 All Rights Reserved
This problem only works in English: Spell the numbers out as words, and count the letters: "one" and "two" each have three letters, and 3×3 = 9. "Three" has five letters and "four" has four; 5×4 = 20. "Five" has four letters and "six" has three; 4×3 = 12. "Seventeen" has nine letters and "twelve" has six, so the missing number is the product of  9 and 6.
This looks like a "math" sequence, but it isn't really. Instead, each term is a description of the preceding term. The first term is just one "1": 11. The second term is two "1's": 21. And so forth:
So the next term is '"312211"'.
*'Find the next number in the following sequence: '1, 11, 21, 1211, 111221,....one 1: 11
two 1's: 21
one 2 and one 1: 1211
one 1, one 2, and two 1's: 111221
three 1's, two 2's, and one 1: 312211
Category:Pre-Calculus
Category:Numbers in a Sequence