Python: Print the length of the series and the series from the given 3rd term, 3rd last term and the sum of a series

Python Basic - 1: Exercise-28 with Solution

Write a Python program to print the length of the series and the series from the given 3rd term, 3rd last term and the sum of a series.

Let X and Y denote the third and the third last term of the arithmetic progression respectively
i.e. X=a+2d and Y=a+(n−3)d where a, d and n are what you would expect them to be.
 Note that we are given X and Y

Now, we are also given the sum of the n terms i.e. S=n2[2a+(n−1)d]

⇒S=n2[(a+2d)+(a+(n−3)d)]

⇒S=n2[X+Y]

⇒n=2SX+Y

Having computed n, we can plug back it's value in the expression for Y. 
This will give us 2 equations in 2 unknowns (a and d) which we can solve to determine the remaining variables.

X=a+2d and Y=a+(2SX+Y−3)d
Reference: https://bit.ly/2N2VM9f

Sample Data:
Input third term of the series: 3
Input 3rd last term: 3
Input Sum of the series: 15
Length of the series: 5
Series:
1 2 3 4 5

Sample Solution:

Python Code:

tn = int(input("Input third term of the series:"))
tltn = int(input("Input 3rd last term:"))
s_sum = int(input("Sum of the series:"))
n = int(2*s_sum/(tn+tltn))
print("Length of the series: ",n)


if n-5==0:
  d = (s_sum-3*tn)//6
else:
  d = (tltn-tn)/(n-5)

a = tn-2*d
j = 0
print("Series:")
for j in range(n-1):
  print(int(a),end=" ")
  a+=d
print(int(a),end=" ")

Sample Output:

Input third term of the series: 3
Input 3rd last term: 6
Sum of the series: 36
Length of the series:  8
Series:
1 2 3 4 5 6 7 8 

More Sample Output:

Input third term of the series: 3
Input 3rd last term: 3
Sum of the series: 15
Length of the series:  5
Series:
1 2 3 4 5

Flowchart:

Python Code Editor:

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