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

Levels of difficulty: / perform operation:

### 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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