C program to compute geometric progression

In C programming, a geometric progression (GP) is a sequence where each term after the first is found by multiplying the previous term by a common ratio. The sum of a geometric progression follows the formula: 1 + x + x² + x³ + ... + x?.

Syntax

sum = 1 + x + x² + x³ + ... + x?

Algorithm

The algorithm to compute geometric progression is as follows −

1. Read values for x (common ratio) and n (number of terms)
2. Initialize sum to 0
3. Use a loop to calculate sum = sum + pow(x, i) for i from 0 to n
4. Display the result

Example

Following is the C program to compute the geometric progression −

#include <stdio.h>
#include <math.h>

int main() {
    int x, n, i;
    double sum = 0.0;
    
    printf("Enter the values for x and n: ");
    scanf("%d %d", &x, &n);
    
    if (n >= 0) {
        for (i = 0; i <= n; i++) {
            sum = sum + pow(x, i);
        }
        printf("x = %d, n = %d<br>", x, n);
        printf("The sum of the geometric progression is: %.0f<br>", sum);
    } else {
        printf("Not a valid n value: %d<br>", n);
    }
    
    return 0;
}

Enter the values for x and n: 4 5
x = 4, n = 5
The sum of the geometric progression is: 1365

Flowchart

Key Points

• The program uses pow() function from math.h to calculate powers
• Loop runs from i = 0 to n (inclusive) to include all terms
• Input validation ensures n is non-negative
• Sum is calculated as: 1 + x¹ + x² + x³ + ... + x?

Conclusion

Computing geometric progression in C involves using a simple loop with the pow() function. This approach efficiently calculates the sum of all terms from x? to x? and provides a clear mathematical demonstration of geometric sequences.