C++ program to find n-th term of series 2, 10, 30, 68, 130 ...

In this problem, we are given an integer N. The task is to find the n-th term in series 2, 10, 30, 68, 130...

Let’s take an example to understand the problem,

Input

N = 7

Output

350

Explanation

The series is 2, 10, 30, 68, 130, 222, 350...

Solution Approach

A simple solution to the problem is by finding the general term of the series. Here, the Nth term of the series is N^3 + N. This is found by subtracting the current element with the current index.

For i,
i = 1, T(1) = 2 = 1 + 1 = 1^3 + 1
i = 2, T(1) = 10 = 8 + 2 = 2^3 + 2
i = 3, T(1) = 30 = 27 + 3 = 3^3 + 2

Program to illustrate the working of our solution,

Example

#include <iostream>
using namespace std;
int findNthTerm(int N) {
   return ((N*N*N) + N);
}
int main() {
   int N = 8;
   cout<<"The "<<N<<"th term of the series is "<<findNthTerm(N);
   return 0;
}

Output

The 8th term of the series is 520