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**Arithmetic progression:**

An Arithmetic progression is a mathematical sequence of numbers in which the difference between the consecutive terms is constant.

In general, an arithmetic sequence looks like this: a, a+d, a+2d, a+3d,…………….

where a = first term

d= common difference

n= number of terms in series

**Formula** : d= second term – first term

The sum of Arithmetic progression Series : Sn = n/2(2a + (n – 1) d)

The Tn (nth term) of Arithmetic progression Series : Tn = a + (n – 1) d

Given a, n, d values and the task is to find the sum of the Arithmetic progression Series.

**Examples:**

**Example 1:**

**Input:**

Given first term = 3 Given total terms = 9 Given common difference = 4

**Output:**

Given Arithmetic Progression Series Sum with [a,n,d]:( 3 9 4 ) = 171.0 The Given Arithmetic Progression Series nth Term with [a,n,d]:( 3 9 4 ) = 35

**Example 2:**

**Input:**

Given first term = 7 Given total terms = 15 Given common difference = 2

**Output:**

Given Arithmetic Progression Series Sum with [a,n,d]:( 7 15 2 ) = 315.0 The Given Arithmetic Progression Series nth Term with [a,n,d]:( 7 15 2 ) = 35

## Program to Find Sum of Arithmetic Progression Series

Below are the ways to find the sum of the Arithmetic progression Series:

### Method #1: Using Mathematical Formula (Static Input)

**Approach: **

- Give the first term of arithmetic progression series as static input and store it in a variable.
- Give the total number of terms of the A.P. series as static input and store it in another variable.
- Give the common difference of the A.P. series as static input and store it in another variable.
- Calculate the sum of the given arithmetic progression series using the above given mathematical formula(
**n/2(2a + (n – 1) d)**) and store it in a variable. - Calculate the nth term of the given arithmetic progression series using the above given mathematical formula (
**Tn = a + (n – 1) d)**and store it in another variable. - Print the sum and nth term of the given Arithmetic Progression series.
- The Exit of the program.

**Below is the implementation:**

# Give the first term of arithmetic progression series as static input # and store it in a variable. fst_trm = 2 # Give the total number of terms of the A.P. series as static input and # store it in another variable. total_terms = 6 # Give the common difference of the A.P. series as static input and store it # in another variable. common_diff = 4 # Calculate the sum of the given arithmetic progression series using the above given # mathematical formula(n/2(2a + (n – 1) d)) and store it in a variable. sum_ap = (total_terms * (2 * fst_trm + (total_terms - 1) * common_diff)) / 2 # Calculate the nth term of the given arithmetic progression series using the above # given mathematical formula ( Tn = a + (n – 1) d) and store it in another variable. nth_trm_ap = fst_trm + (total_terms - 1) * common_diff # Print the sum and nth term of the given Arithmetic Progression series. print("Given Arithmetic Progression Series Sum with [a,n,d]:(", fst_trm, total_terms, common_diff, ") = ", sum_ap) print("The Given Arithmetic Progression Series nth Term with [a,n,d]:(", fst_trm, total_terms, common_diff, ") = ", nth_trm_ap)

**Output:**

Given Arithmetic Progression Series Sum with [a,n,d]:( 2 6 4 ) = 72.0 The Given Arithmetic Progression Series nth Term with [a,n,d]:( 2 6 4 ) = 22

### Method #2: Using Mathematical Formula (User Input)

**Approach: **

- Give the first term of arithmetic progression series as user input using the int(input()) function and store it in a variable.
- Give the total number of terms of the A.P. series as user input using the int(input()) function and store it in another variable.
- Give the common difference of the A.P. series as user input using the int(input()) function and store it in another variable.
- Calculate the sum of the given arithmetic progression series using the above given mathematical formula(
**n/2(2a + (n – 1) d)**) and store it in a variable. - Calculate the nth term of the given arithmetic progression series using the above given mathematical formula (
**Tn = a + (n – 1) d)**and store it in another variable. - Print the sum and nth term of the given Arithmetic Progression series.
- The Exit of the program.

**Below is the implementation:**

# Give the first term of arithmetic progression series as user input using the # int(input()) function and store it in a variable. fst_trm = int(input("Enter some random number = ")) # Give the total number of terms of the A.P. series as user input using the int(input()) function and store # it in another variable. total_terms = int(input("Enter some random number = ")) # Give the common difference of the A.P. series as user input using the int(input()) function and # store it in another variable. common_diff = int(input("Enter some random number = ")) # Calculate the sum of the given arithmetic progression series using the above given # mathematical formula(n/2(2a + (n – 1) d)) and store it in a variable. sum_ap = (total_terms * (2 * fst_trm + (total_terms - 1) * common_diff)) / 2 # Calculate the nth term of the given arithmetic progression series using the above # given mathematical formula ( Tn = a + (n – 1) d) and store it in another variable. nth_trm_ap = fst_trm + (total_terms - 1) * common_diff # Print the sum and nth term of the given Arithmetic Progression series. print("Given Arithmetic Progression Series Sum with [a,n,d]:(", fst_trm, total_terms, common_diff, ") = ", sum_ap) print("The Given Arithmetic Progression Series nth Term with [a,n,d]:(", fst_trm, total_terms, common_diff, ") = ", nth_trm_ap)

**Output:**

Enter some random number = 3 Enter some random number = 9 Enter some random number = 4 Given Arithmetic Progression Series Sum with [a,n,d]:( 3 9 4 ) = 171.0 The Given Arithmetic Progression Series nth Term with [a,n,d]:( 3 9 4 ) = 35

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