In this tutorial, we will discuss a Python program to find the sum of a geometric progression (GP) .

Before going to the program first, let us understand what is a Geometric Progression(GP).

Geometric Progression(GP):

• A geometric progression is a sequence of numbers where each term after the first is found by multiplying the previous term by a constant called the common ratio.
• The sum of the first $n$ terms of a GP is given by the formula: Sn=a(1−rn1−r)S_n = a \left(\frac{1 – r^n}{1 – r}\right)Sn​=a(1−r1−rn​) for r≠1r \neq 1r=1, where $a$ is the first term and $r$ is the common ratio.

Related: Python Program for Simple Calculator

Program code for Geometric Progression in Python

# Sum of a Geometric Progression in Python
def sum_of_gp(a, r, n):
    if r == 1:
        return a * n
    else:
        return a * (1 - r ** n) / (1 - r)

a = float(input("Enter the first term (a): "))
r = float(input("Enter the common ratio (r): "))
n = int(input("Enter the number of terms (n): "))

sum_gp = sum_of_gp(a, r, n)
print(f"The sum of the first {n} terms of the GP is {sum_gp}.")

Explanation

1. Function Definition: The sum_of_gp function takes three parameters: a, r, and n, and returns the sum of the first $n$ terms of the GP.
2. Main Program: The program prompts the user to enter the first term, common ratio, and number of terms. It then calculates the sum of the GP using the sum_of_gp function and prints the result.

Output

• When you run the above program, it will prompt you to enter the first term, common ratio, and number of terms.
• After entering the values, it will calculate the sum of the GP and print the result.

Conclusion

• In this tutorial, we learned how to find the sum of a geometric progression (GP) using a Python program.
• Understanding this concept is essential for solving various mathematical problems and enhancing your programming skills.