 # Python Program to Find the Missing Term of any Arithmetic Progression

In the previous article, we have discussed Python Program to Find Strong Numbers in a List
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

Formula : d= second term – first term

Given an Arithmetic series, and the task is to find the missing term in the given series.

Examples:

Example 1:

Input:

Given Arithmetic Progression series = [10, 14, 18, 22, 30]

Output:

The missing term in the given Arithmetic Progression series is:
26

Example 2:

Input:

Given Arithmetic Progression series = [100, 300, 400, 500, 600, 700]

Output:

The missing term in the given Arithmetic Progression series is:
200

## Program to Find the missing term of any Arithmetic progression

Below are the ways to find the missing term in the given Arithmetic progression series.

### Method #1: Using For Loop (Static Input)

Approach:

• Give the list ( Arithmetic Progression series) as static input and store it in a variable.
• Calculate the length of the given series using the built-in len() function and store it in another variable.
• Calculate the common difference by finding the difference between the list’s last and first terms and divide by N and store it in another variable.
• Take a variable, initialize it with the first term of the given list and store it in another variable say “first term”.
• Loop from 1 to the length of the given list using for loop.
• Inside the loop, check if the difference between the list(iterator) and “first term” is not equal to the common difference using if conditional statement.
• If the statement is true, print the sum of “first term” and common difference
• Else update the value of variable “first term”  by iterator value.
• The Exit of the program.

Below is the implementation:

# Give the list ( Arithmetic Progression series) as static input and store it in a variable.
gvn_lst = [100, 200, 400, 500, 600, 700]
# Calculate the length of the given series using the built-in len() function
# and store it in another variable.
lst_len = len(gvn_lst)
# Calculate the common difference by finding the difference between the list's last and
# first terms and divide by N and store it in another variable.
commn_diff = int((gvn_lst[lst_len-1]-gvn_lst)/lst_len)
# Take a variable, initialize it with the first term of the given list and store
# it in another variable say "first term".
fst_term = gvn_lst
# Loop from 1 to the length of the given list using for loop.
print("The missing term in the given Arithmetic Progression series is:")
for itr in range(1, lst_len):
# Inside the loop, check if the difference between the list(iterator) and "first term"
# is not equal to the common difference using if conditional statement.
if gvn_lst[itr]-fst_term != commn_diff:
# If the statement is true, print the sum of "first term" and common difference
print(fst_term+commn_diff)
break
else:
# Else update the value of variable "first term"  by iterator value.
fst_term = gvn_lst[itr]


Output:

The missing term in the given Arithmetic Progression series is:
26

### Method #2: Using For Loop (User Input)

Approach:

• Give the list ( Arithmetic Progression series) as user input using list(),map(),input(),and split() functions and store it in a variable.
• Calculate the length of the given series using the built-in len() function and store it in another variable.
• Calculate the common difference by finding the difference between the list’s last and first terms and divide by N and store it in another variable.
• Take a variable, initialize it with the first term of the given list and store it in another variable say “first term”.
• Loop from 1 to the length of the given list using for loop.
• Inside the loop, check if the difference between the list(iterator) and “first term” is not equal to the common difference using if conditional statement.
• If the statement is true, print the sum of “first term” and common difference
• Else update the value of variable “first term”  by iterator value.
• The Exit of the program.

Below is the implementation:

#Give the list ( Arithmetic Progression series) as user input using list(),map(),input(),and split()
#functions and store it in a variable.
gvn_lst = list(map(int, input( 'Enter some random List Elements separated by spaces = ').split()))
# Calculate the length of the given series using the built-in len() function
# and store it in another variable.
lst_len = len(gvn_lst)
# Calculate the common difference by finding the difference between the list's last and
# first terms and divide by N and store it in another variable.
commn_diff = int((gvn_lst[lst_len-1]-gvn_lst)/lst_len)
# Take a variable, initialize it with the first term of the given list and store
# it in another variable say "first term".
fst_term = gvn_lst
# Loop from 1 to the length of the given list using for loop.
print("The missing term in the given Arithmetic Progression series is:")
for itr in range(1, lst_len):
# Inside the loop, check if the difference between the list(iterator) and "first term"
# is not equal to the common difference using if conditional statement.
if gvn_lst[itr]-fst_term != commn_diff:
# If the statement is true, print the sum of "first term" and common difference
print(fst_term+commn_diff)
break
else:
# Else update the value of variable "first term"  by iterator value.
fst_term = gvn_lst[itr]


Output:

Enter some random List Elements separated by spaces = 100 300 400 500 600 700
The missing term in the given Arithmetic Progression series is:
200

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