C program for calculating the Nth term of a geometric sequence

Given 'a' the First term, 'r' the common ratio and 'n' for the number of terms in a series. The task is to find the nth term of the series .

So, before discussing how to write a program for the problem first we should know what is Geometric Progression.

Geometric progression or Geometric sequence in mathematics are where each term after the first term is found by multiplying the previous one with the common ratio for a fixed number of terms.

Like 2, 4, 8, 16, 32.. is a geometric progression with first term 2 and common ratio 2. If we have n = 4 then the output will be 16.

So, we can say that Geometric Progression for nth term will be like −

GP1 = a1
GP2 = a1 * r^(2-1)
GP3 = a1 * r^(3-1)
. . .
GPn = a1 * r^(n-1)

So the formula will be GP = a * r^ (n-1).

Example

Input: A=1
   R=2
   N=5
Output: The 5th term of the series is: 16
Explanation: The terms will be
   1, 2, 4, 8, 16 so the output will be 16
Input: A=1
   R=2
   N=8
Output: The 8<sup>th</sup> Term of the series is: 128

The method we will use to solve the given problem −

• Take the first The term A, the common ratio R, and the number of sequences N.
• Then calculate the nth item through A * (int)(pow(R, N - 1).
• Return the output obtained by the above calculation.

Algorithm

Start
   Step 1 -> In function int Nth_of_GP(int a, int r, int n)
      Return( a * (int)(pow(r, n - 1))
   Step 2 -> In function int main()
      Declare and set a = 1
      Declare and set r = 2
      Declare and set n = 8
      Print The output returned from calling the function Nth_of_GP(a, r, n)
Stop

Example

#include <stdio.h>
#include <math.h>
//function to return the nth term of GP
int Nth_of_GP(int a, int r, int n) {
   // the Nth term will be
   return( a * (int)(pow(r, n - 1)) );
}
//Main Block
int main() {
   // initial number
   int a = 1;
   // Common ratio
   int r = 2;
   // N th term to be find
   int n = 8;
   printf("The %dth term of the series is: %d</p><p>",n, Nth_of_GP(a, r, n) );
   return 0;
}

Output

The 8th term of the series is: 128

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