# C Program To Compute Sum Of Geometric Progression

This program receive two numbers and compute the sum of geometric progression. The program implements the geometric progression and output the results when it receives the inputs.

Learn C programming concepts before you start with this example program. Continue reading if you are familiar with the basics.

### Problem Definition

A geometric progression has two conditions.

1. $a_1 = a$ where $a$ is the first term and not equal to 0.
2. $a_n = a_{n-1}r$ for $n \geq 1$

r is called the common ratio.

Suppose $a = 1$ and $r = 5$, then

$a_1=1, a_2= 5, a_3=25, a_4= 125$

Basically, you can compute any term using the following formula.

$a_n \hspace{1ex} = \hspace{1ex} a \cdot \hspace{1ex} r_{n-1}$

Once the program obtains the value of each term up to $n$, it add all the value and prints the output. The expression that this program evaluates is

 $1\hspace{1ex} + \hspace{1ex} x \hspace{1ex} + \hspace{1ex} x^2\hspace{1ex} + \hspace{1ex} x^3 \hspace{1ex} + \hspace{1ex} x^4 \hspace{1ex} + \hspace{1ex} ... \hspace{1ex} + \hspace{1ex} x^{n-1} \hspace{1ex} ...$
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### Program Source Code

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
int main()
{
int geo_sum, i, x,n;
geo_sum = 1;
printf("Enter the value for x:");
scanf("%d",&x);
printf("Enter the value for n:");
scanf("%d",&n);
if(n <= 0 || x <= 0)
{
printf("Incorrect Value!!\n\n");
}
else
{
printf("The value is valid!!\n\n");
}
for(i = 1;i <= n; i++)
{
geo_sum = geo_sum + pow(x,i);
}
printf("The Sum of Series = %d\n",geo_sum);
system("PAUSE");
return 0;
}

### Output

The input values for the program is r = x = 2 and n = 10. If we use the values in the geometric expression as follows.

1 + 2 + 22 + 23 + 24 + 25 + 26 + 27 + 28 + 29
= 1  + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512 + 1024
= 2047

Therefore, the output is correct.

Enter the value for x:2
Enter the value for n:10
The value is valid!!
The Sum of Series = 2047
Press any key to continue . . . _