# Python Program to find the Sum of Arithmetic Progression

In this tutorial, we will discuss a Python program to find the sum of an arithmetic progression (AP).

Before going to the program first, let us understand what is an Arithmetic Progression(AP).

Arithmetic Progression (AP):

• An arithmetic progression is a sequence of numbers in which the difference between consecutive terms is constant.
• The sum of the first nn terms of an AP is given by the formula: Sn=n2(2a+(n−1)d)S_n = \frac{n}{2} \left(2a + (n – 1)d\right), where aa is the first term and dd is a common difference.

#### Program code for Arithmetic Progression in Python

# Sum of an Arithmetic Progression in Python
def sum_of_ap(a, d, n):
return (n / 2) * (2 * a + (n - 1) * d)

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

sum_ap = sum_of_ap(a, d, n)
print(f"The sum of the first {n} terms of the AP is {sum_ap}.")



#### Explanation

1. Function Definition: The sum_of_ap function takes three parameters: a, d, and n, and returns the sum of the first nn terms of the AP.
2. Main Program: The program prompts the user to enter the first term, common difference, and number of terms. It then calculates the sum of the AP using the sum_of_ap function and prints the result.

#### Output

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

#### Conclusion

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