Arithmetic Progression:
The Arithmetic Series is a term series in which the next item is formed by adding a common difference to the previous item.
The A.P. series is a numerical sequence in which the difference between any two consecutive numbers is always the same. This is referred to as a common difference.
Formulas:
The sum of AP ( Sn ) = n/2(2a + (n – 1) d) Nth term (Tn) = a + (n – 1) d
where a = first term
d = common difference
n= number of terms
Given a, d, n values, and the task is to calculate the Arithmetic progression series.
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Program for Arithmetic Progression in Python
Method #1: Using Mathematical Formula (Static Input)
1)Printing the first n terms of Arithmetic Progression:
Approach:
- Give the first term (a) as static input and store it in a variable.
- Give a common difference (d) as static input and store it in another variable.
- Give the number of terms(n) as static input and store it in another variable.
- loop from 1 to gvn_n+1 using the for loop(excludes last no).
- Inside the for loop, calculate the nth term of AP using the above-given mathematical formula and store it in a variable.
- Print the above result.
- Print the nth term of AP.
- The Exit of the Program.
Below is the implementation:
# Give the first term (a) as static input and store it in a variable. gvn_a = 2 # Give the common difference (d) as static input and store it in another variable. gvn_d = 3 # Give the number of terms(n) as static input and store it in another variable. gvn_n = 7 # loop from 1 to gvn_n+1 using the for loop(excludes last no) for itr in range(1, gvn_n+1): # Inside the for loop, calculate the nth term of AP using the above given # mathematical formula and store it in a variable. nth_term = gvn_a + (itr-1)*gvn_d # Print the above result print(nth_term) # Print the nth term of AP print("The nth_term of AP = ", nth_term)
Output:
2 5 8 11 14 17 20 The nth_term of AP = 20
2)Calculating the sum of AP
Approach:
- Give the first term (a) as static input and store it in a variable.
- Give a common difference (d) as static input and store it in another variable.
- Give the number of terms(n) as static input and store it in another variable.
- Calculate the sum of n terms of AP using the above given mathematical formula and store it in a variable.
- Print the Sum of Arithmetic Progression(AP) of given n terms.
- The Exit of the Program.
Below is the implementation:
# Give the first term (a) as static input and store it in a variable. gvn_a = 2 # Give the common diiference (d) as static input and store it in another variable. gvn_d = 3 # Give the number of terms(n) as static input and store it in another variable. gvn_n = 7 # Calculate the sum of n terms of AP using the above given mathematical formula # and store it in a variable. Sum_Ap = (gvn_n/2)*(2*gvn_a + (gvn_n-1)*gvn_d) # Print the Sum of Arithmetic Progression(AP) of given n terms. print("The Sum of Arithmetic Progression(AP) of given n terms = ", Sum_Ap)
Output:
The Sum of Arithmetic Progression(AP) of given n terms = 77.0
Method #2: Using Mathematical Formula (User Input)
1)Printing the first n terms of Arithmetic Progression:
Approach:
- Give the first term (a) as user input using the int(input()) function and store it in a variable.
- Give a common difference (d) as user input using the int(input()) function and store it in another variable.
- Give the number of terms(n) as user input using the int(input()) function and store it in another variable.
- loop from 1 to gvn_n+1 using the for loop(excludes last no).
- Inside the for loop, calculate the nth term of AP using the above-given mathematical formula and store it in a variable.
- Print the above result.
- Print the nth term of AP.
- The Exit of the Program.
Below is the implementation:
# Give the first term (a) as user input using the int(input()) function and store it in a variable. gvn_a = int(input("Enter some random number = ")) # Give the common difference (d) as user input using the int(input()) function and # store it in another variable. gvn_d = int(input("Enter some random number = ")) # Give the number of terms(n) as user input using the int(input()) function and # store it in another variable. gvn_n = int(input("Enter some random number = ")) # loop from 1 to gvn_n+1 using the for loop(excludes last no) for itr in range(1, gvn_n+1): # Inside the for loop, calculate the nth term of AP using the above given # mathematical formula and store it in a variable. nth_term = gvn_a + (itr-1)*gvn_d # Print the above result print(nth_term) # Print the nth term of AP print("The nth_term of AP = ", nth_term)
Output:
Enter some random number = 1 Enter some random number = 2 Enter some random number = 12 1 3 5 7 9 11 13 15 17 19 21 23 The nth_term of AP = 23
2)Calculating the sum of AP
Approach:
- Give the first term (a) as user input using the int(input()) function and store it in a variable.
- Give a common difference (d) as user input using the int(input()) function and store it in another variable.
- Give the number of terms(n) as user input using the int(input()) function and store it in another variable.
- Calculate the sum of n terms of AP using the above given mathematical formula and store it in a variable.
- Print the Sum of Arithmetic Progression(AP) of given n terms.
- The Exit of the Program.
Below is the implementation:
# Give the first term (a) as user input using the int(input()) function and store it in a variable. gvn_a = int(input("Enter some random number = ")) # Give the common difference (d) as user input using the int(input()) function and # store it in another variable. gvn_d = int(input("Enter some random number = ")) # Give the number of terms(n) as user input using the int(input()) function and # store it in another variable. gvn_n = int(input("Enter some random number = ")) # Calulate the sum of nterms of AP using the above given mathematical formula # and store it in a variable. Sum_Ap = (gvn_n/2)*(2*gvn_a + (gvn_n-1)*gvn_d) # Print the Sum of Arithmetic Progression(AP) of given n terms. print("The Sum of Arithmetic Progression(AP) of given n terms = ", Sum_Ap)
Output:
Enter some random number = 1 Enter some random number = 2 Enter some random number = 12 The Sum of Arithmetic Progression(AP) of given n terms = 144.0