# 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

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

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**Previous:** Write a Python program to find the type of the progression (arithmetic progression/geometric progression) and the next successive member of a given three successive members of a sequence.

**Next:** Write a Python program to find common divisors between two numbers in a given pair.

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