Question

Prove that be n th term of an A.P can not be n^2+1. Justify your answer.

Answer 1

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 n2 + 1.