Program to find N-th term of series 2, 12, 28, 50, 77, 112, 152, 198, …in C++

In this problem, we are given a number N. Our task is to create a program to find N-th term of series 2, 12, 28, 50, 77, 112, 152, 198, …in C++.

Problem Description − To find the N-th term of the series.

2, 12, 28, 50, 77, 112, 152, 198, ...N terms

We will find a general for the series.

Let’s take an example to understand the problem,

Input − N = 6

Output − 112

Solution Approach:

Here, the series is increasing in parabolic form, so the general term will be a quadratic equation.

So, the general formula for the series is

T_N = 3*(N*N) + N - 2

Program to illustrate the working of our solution,

#include <iostream>
using namespace std;
int findNTerm(int N) {
int nthTerm = ( (3*N*N) + N - 2);
return nthTerm;
}
int main()
{
int N = 10;
cout<<N<<"th term of the series is "<<findNTerm(N);
return 0;
}

Output:

10th term of the series is 308