This tutorial guides you through writing a C program to find the sum of a Geometric Progression (GP) series. You'll learn two approaches: using a formula and using a loop. The tutorial will also cover the logic and concept behind the program and provide examples and code snippets.

## What is Geometric Progression (GP) Series

A Geometric Progression (GP) is a mathematical concept that involves a sequence of numbers following a specific pattern. The pattern is based on multiplying the previous term by a fixed number, known as the common ratio. For example, consider the sequence 2, 6, 18, 54, and so on, which is a geometric progression with a common ratio of 3. GP is commonly found in mathematical and scientific applications, and understanding their properties is essential in solving many problems in these fields.

## Methods to Find Sum of GP Series

Two methods are commonly used to find the sum of geometric progressions: **using a formula** or **a loop**.

## Method 1: Using a Formula

The sum of a GP series can be calculated using the following formula:

```
S = a(1 - r^n) / (1 - r)
```

Where the first term is `a`

, the common ratio is `r`

, and the number of terms is `n`

.

### C Program to Find the Sum of a GP Series Using a Formula

To use the above formula in C, you need to include the `math.h`

header file, which provides the `pow()`

function to calculate the power of a number. You also need to declare and initialize the variables for the first term, the common ratio, and the number of terms, and then use the formula to calculate and print the `sum`

.

The following code snippet shows how to use the formula to find the sum of a GP series in C:

```
#include <stdio.h>
#include <math.h>
int main() {
float a, r, n, sum; // Variables for first term, ratio, number of terms, sum
// Input: first term
printf("Enter the first term: ");
scanf("%f", &a);
// Input: common ratio
printf("Enter the common ratio: ");
scanf("%f", &r);
// Input: number of terms
printf("Enter the number of terms: ");
scanf("%f", &n);
sum = (a * (1 - pow(r, n))) / (1 - r); // Calculate sum of GP
printf("The sum of the GP series is: %.2f", sum); // Output sum
return 0; // Program end
}
```

Program Output:

```
Enter the first term: 2
Enter the common ratio: 3
Enter the number of terms: 5
The sum of the GP series is: 242.00
```

Explanation:

In the above program, we declare four variables: `a`

, `r`

, `n`

, and `sum`

. Afterwards, we prompt the user to input the first term, common ratio, and number of terms. Using the earlier formula, we calculate the GP series sum and store the result in the `sum`

variable. We utilize the `printf()`

function to display the GP series sum.

## Method 2: Using a Loop

Another way to find the sum of a GP series is to use a loop that iterates over the terms of the series and adds them to a variable that stores the sum.

### C Program to Find the Sum of a GP Series Using a Loop

The following code snippet shows how to use a for loop to find the sum of a GP series in C:

```
#include <stdio.h>
int main() {
float a, r, n, sum = 0, term; // Variables for first term, ratio, number of terms, sum
// Input: first term
printf("Enter the first term: ");
scanf("%f", &a);
// Input: common ratio
printf("Enter the common ratio: ");
scanf("%f", &r);
// Input: number of terms
printf("Enter the number of terms: ");
scanf("%f", &n);
term = a; // Initialize term
for (int i = 1; i <= n; i++) {
sum += term; // Add term to sum
term *= r; // Update term
}
printf("The sum of the GP series is: %.2f", sum); // Output sum
return 0; // Program end
}
```

## Conclusion

This tutorial taught you how to calculate the sum of a geometric progression series using two different methods in C programming, enhancing your understanding of series and sequences.