# C++ program to find n-th term in the series 7, 15, 32, …

C++Server Side ProgrammingProgramming

In this problem, we are given an integer N. The task is to find n-th term in series 7, 15, 32....

Let’s take an example to understand the problem,

## Input

N = 6

## Output

281

## Explanation

The series upto nth term is 7, 15, 32, 67, 138, 281

## Solution Approach

The solution to the problem lies in decoding the series. You can see the series is a mix of series.

The subtracting the values,

T(2) - T(1) = 15 - 7 = 8
T(3) - T(2) = 32 - 15 = 17

So, T(2) = 2*T(1) + 1
T(3) = 2*T(2) + 2

T(n) = 2*T(n-1) + (n-1)

So, the value of the nth term is found using the last term. To find these we will loop from 1 to n and find each value of the series.

Program to illustrate the working of our solution,

## Example

Live Demo

#include <iostream>
using namespace std;
int findNthTerm(int n) {
if (n == 1)
return 7;
int termN = 7;
for (int i = 2; i <= n; i++)
termN = 2*termN + (i - 1);
return termN;
}
int main(){
int n = 12;
cout<<"The series is 7, 15, 32, 67...\n";
cout<<n<<"th term of the series is "<<findNthTerm(n);
return 0;
}

## Output

The series is 7, 15, 32, 67...
12th term of the series is 18419