Question

Prove that the nth term of an A.P, cannot be n^2 + 1. Justify your answer !!

Answer 1

The nth term of an AP can’t be n^2+1.

Justification:

Substitute n= 1, 2, 3,... in the series would be

1^2 + 1, 2^2 + 1, 3^2 + 1, …......

2, 5,10,..............

Difference between first and second term = 5 - 2 = 3.

And difference between second and third term = 10 - 5 = 5

Their common difference is not equal.

In A.P,common difference should  be equal, so this series can’t be A.P.

Thus, the nth term of an A.P. can’t be n^2 + 1

Answer 2

hope you understand