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In this problem, we are given an integer N. The task is to find the n-th term in series 3, 9, 21, 41, 71...

**Let’s take an example to understand the problem,**

N = 7

169

The series is 3, 9, 21, 41, 71, 169...

A simple solution to the problem is by finding the general term of the series. The general term can be found by observing the series a bit. It is,

$$T(N) = \sum n^{2} + \sum n + 1$$

We can directly use the formula for the sum of square of first n natural numbers, first n natural number and then add the three values. At last return the resultant value,

$$T(N)=\left(\frac{n*(n+1)*(2n+1)}{6}\right)+\left(\frac{n*(n+1)}{2}\right)+1$$

**Program to illustrate the working of our solution,**

#include <iostream> using namespace std; int findNthTerm(int n) { return ((((n)*(n + 1)*(2*n + 1)) / 6) + (n * (n + 1) / 2) + 1); } int main() { int N = 12; cout<<"The "<<N<<"th term of the series is "<<findNthTerm(N); return 0; }

The 12th term of the series is 729

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