Program to find N-th term in the given series in C++

In this problem, we are given a number N. Our task is to create a program to find N-th term in the given series in C++.

Problem Description

To find the sum of the given series −

1, 1, 2, 3, 4, 9, 8, 27, 16, 81, 32, 243, 64, 729, 128, 2187, 256, ... NTerms

We will find the general term of the series.

Let’s take an example to understand the problem,

Example 1

Input

N = 6

Output

9

Example 2

Input

N = 13

Output

64

Solution Approach

To solve the problem, we need to carefully observe the series. As it is, a mixture series and these types of series are difficult to recognize initially but later it is easy to work with.

The series is a mixture series of the at type,

At even places, the index of the series is a series of powers of 3.

At odd places, the index of the series is a series of powers of 2.

The general term is derived as −

T_{N}=2^{N/2}, if N is odd.

3^{N/2}, if N is even.

Example

 Live Demo

#include <iostream> #include <math.h> using namespace std; int findLCM(int a, int b) {    int LCM = a, i = 2;    while(LCM % b != 0) {       LCM = a*i;       i++;    }    return LCM; } int findNTerm(int N) {    if(N%2 == 0){       return pow(3, ((N-1)/2));    }    else       return pow(2, (N/2)); } int main() {    int N = 9;    cout<<N<<"th term of the series is "<<findNTerm(N)<<endl; N = 14; cout<<N<<"th term of the series is "<<findNTerm(N); }

Output

9th term of the series is 16 14th term of the series is 729