Write a c program to find out the sum of given G.P.


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Definition of geometric progression (G.P.):

A series of numbers in which ratio of any two consecutive numbers is always a same number that is constant. This constant is called as common ratio.

Example of G.P. series:

2 4 8 16 32 64
Here common difference is 2 since ratio any two consecutive numbers for example 32 / 16 or 64/32 is 2.

Sum of G.P. series:

Sn =a(1–rn+1)/(1-r)

Tn term of G.P. series:

Tn = arn-1   

Sum of infinite G.P. series:


Sn = a/(1-r)  if 1 > r
= a/(r-1) if r > 1

C Program

#include<stdio.h>
#include<math.h>
int main() {
	float a,r,i,tn;
	int n;
	float sum=0;
	printf("Enter the first number of the G.P. series: ");
	scanf("%f",&a);
	printf("Enter the total numbers in the G.P. series: ");
	scanf("%d",&n);
	printf("Enter the common ratio of G.P. series: ");
	scanf("%f",&r);
	sum = (a*(1 - pow(r,n+1)))/(1-r);
	tn = a * (1 -pow(r,n-1));
	printf("tn term of G.P.: %f",tn);
	printf("\nSum of the G.P.: %f",sum);
	return 0;
}

Output:

Enter the first number of the G.P. series: 1
Enter the total numbers in the G.P. series: 5
Enter the common ratio of G.P. series: 2
tn term of G.P. : 16.000000
Sum of the G.P. : 63.000000





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