Find pth Term of a GP Given mth and nth Terms in C++

In this problem we are given five values m, n, mth term, nth term, p. Our task is to Find Pth term of a GP if Mth and Nth terms are given.

For a GP, we are given the values of mth term and nth term. Using these values, we need to find the Pth term of the series.

Let’s take an example to understand the problem,

Input

m = 7, mthTerm = 1458, n = 10, nthterm = 39366, p = 3

Output

18

Solution Approach

Here, we are given a GP. let's suppose the GP is,

GP = a , a*r , a*(r2), a*(r3) ….

The formula for T^th term is

Tth Term = a * r(T-1)

Now, we are given nth and mth term,

mth term = a * (r ^ (m-1))
nth term = a * (r ^ (n-1))

Dividing the equations we get,

mth term / nth term = (r ^(m - n))

Using this equation, we can find the value of r, Then a can be found using the value of mth term as

mth term = a * (r^(m-1))

Then after finding the value of a and r. The value of pth term can be easily found using,

pth term = a * (r^(p-1))

Program to illustrate the working of our solution,

Example

 Live Demo

#include <cmath>
#include <iostream>
using namespace std;
double findRinGP(double m, double n, double mth, double nth) {
   if (m < n)
      return pow(nth / mth, 1.0 / (n - m));
   return pow(mth / nth, 1.0 / (m - n));
}
double findTermGP(int m, int n, double mth, double nth, int p) {
   double r = findRinGP(m, n, mth, nth);
   double a = mth / pow(r, (m - 1));
   return ( a * pow(r, (p - 1)) );
}
int main() {
   int m = 7, n = 10, p = 5;
   double mth = 1458, nth = 39366;
   cout<<"The "<<p<<"th of the series is "<<findTermGP(m, n, mth, nth, p);
   return 0;
}

Output

The 5th of the series is 162