### 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