Program to find Sum of the series 1*3 + 3*5 + .... - GeeksforGeeks

01 Nov, 2021
Given a series:  
Sn = 1*3 + 3*5 + 5*7 + ... 
It is required to find the sum of first n terms of this series represented by Sn, where n is given taken input.Examples:  
Input : n = 2 
Output : S<sub>n</sub> = 18
Explanation:
The sum of first 2 terms of Series is
1*3 + 3*5
= 3 + 15 
= 28

Input : n = 4 
Output : S<sub>n</sub> = 116
Explanation:
The sum of first 4 terms of Series is
1*3 + 3*5 + 5*7 + 7*9
= 3 + 15 + 35 + 63
= 116
Let, the n-th term be denoted by tn. This problem can easily be solved by observing that the nth term can be founded by following method: 
tn = (n-th term of (1, 3, 5, ... ) )*(nth term of (3, 5, 7, ....))
Now, n-th term of series 1, 3, 5 is given by 2*n-1 and, the n-th term of series 3, 5, 7 is given by 2*n+1Putting these two values in tn: 
tn = (2*n-1)*(2*n+1) = 4*n*n-1
Now, the sum of first n terms will be given by : 
Sn = ∑(4*n*n – 1) =∑4*{n*n}-∑(1)
Now, it is known that the sum of first n terms of series n*n (1, 4, 9, ...) is given by: n*(n+1)*(2*n+1)/6 And sum of n number of 1’s is n itself.Now, putting values in Sn: 
Sn = 4*n*(n+1)*(2*n+1)/6 – n = n*(4*n*n + 6*n – 1)/3
Now, Sn value can be easily found by putting the desired value of n.Below is the implementation of the above approach:  
C++
Java
Python
C#
PHP
Javascript
// C++ program to find sum of first n terms#include <bits/stdc++.h>using namespace std; int calculateSum(int n){    // Sn = n*(4*n*n + 6*n - 1)/3    return (n * (4 * n * n + 6 * n - 1) / 3);} int main(){    // number of terms to be included in the sum    int n = 4;     // find the Sn    cout << "Sum = " << calculateSum(n);     return 0;}
// Java program to find sum// of first n termsclass GFG{    static int calculateSum(int n)    {        // Sn = n*(4*n*n + 6*n - 1)/3        return (n * (4 * n * n +                     6 * n - 1) / 3);    }     // Driver Code    public static void main(String args[])    {        // number of terms to be        // included in the sum        int n = 4;             // find the Sn        System.out.println("Sum = " +                            calculateSum(n));    }} // This code is contributed by Bilal
# Python program to find sum# of first n termsdef calculateSum(n):         # Sn = n*(4*n*n + 6*n - 1)/3    return (n * (4 * n * n +                 6 * n - 1) / 3); # Driver Code # number of terms to be# included in the sumn = 4 # find the Snprint("Sum =",calculateSum(n)) # This code is contributed by Bilal
// C# program to find sum// of first n termsusing System; class GFG{ static int calculateSum(int n){    // Sn = n*(4*n*n + 6*n - 1)/3    return (n * (4 * n * n +                 6 * n - 1) / 3);} // Driver codestatic public void Main (){    // number of terms to be    // included in the sum    int n = 4;     // find the Sn    Console.WriteLine("Sum = " +                       calculateSum(n));}} // This code is contributed// by mahadev
<?php// PHP program to find sum// of first n terms function calculateSum($n){    // Sn = n*(4*n*n + 6*n - 1)/3    return ($n * (4 * $n * $n +                  6 * $n - 1) / 3);} // number of terms to be// included in the sum$n = 4; // find the Snecho "Sum = " . calculateSum($n); // This code is contributed// by ChitraNayal?>
<script> // Javascript program to find sum// of first n terms     function calculateSum( n) {        // Sn = n*(4*n*n + 6*n - 1)/3        return (n * (4 * n * n + 6 * n - 1) / 3);    }     // Driver Code              // number of terms to be        // included in the sum        let n = 4;         // find the Sn        document.write("Sum = " + calculateSum(n));         // This code contributed by Princi Singh </script>
Sum = 116
 
Time Complexity: O(1)
Auxiliary Space: O(1)
bilal-hungund
Mahadev99
ukasp
princi singh
souravmahato348
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