Program to find N-th term of series 3, 6, 18, 24, ... 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 3, 6, 18, 24, … in C++.

Problem Description − To find the Nth term of the series −

3, 6, 18, 24, 45, 54, 84 … N Terms

We need to find the general formula for the given series.

Let’s take an example to understand the problem,

Input − N = 10

Output − 150

Solution Approach:

To find the general term of the series, we will first observe the series and check all the possible generalizations of the series. Like, 3 is common in all but as you go-ahead, you will find that it will not provide any result.

Here, we can also take out the term n i.e. 1, 2, 3. From their values in series to give it a new form. Further checking the remaining value, we will get the following general formula.

General Term of the series

T<sub>n</sub> = (n*((n/2) + ((n%2) *2) + 5))

Example

#include <iostream>
using namespace std;
int findNTerm(int N) {
   int nthTerm = ( N*((N/2)+ ((N%2)*2) + N) );
   return nthTerm;
}
int main() {
   int N = 7;
   cout<<N<<"th term of the series is "<<findNTerm(N);
   return 0;
}

Output:

7th term of the series is 84