## Pages

### write a c program to find out the sum of infinite G.P. series | CTechnotips

#include<stdio.h>

int main(){
float a,r;
float sum=0;
printf("Enter the first number of the G.P. series: ");
scanf("%f",&a);
printf("Enter the common ratio of G.P. series: ");
scanf("%f",&r);
if(1 > r)
sum = a/(1-r);
else
sum = a/(r-1);
printf("\nSum of the infinite G.P. series: %f",sum);
return 0;
}

Sample output:

Enter the first number of the G.P. series: 1
Enter the common ratio of G.P. series: .5
Sum of the infinite G.P. series: 2.000000
Enter the first number of the G.P. series: 5
Enter the common ratio of G.P. series: 2
Sum of the infinite G.P. series: 5.000000

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