# Python Program to find the Sum of Geometric Progression

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 nn 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) for r≠1r \neq 1, where aa is the first term and rr is the common ratio.

#### 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 nn 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.