Question

Following are APs or not? If they form an A.P. find the common difference d and write three more terms: 

1², 5², 7², 73 …

Answer 1

1², 5², 7², 73 …

Or 1, 25, 49, 73 …

It can be observed that

a₂ − a₁ = 25 − 1 = 24

a₃ − a₂ = 49 − 25 = 24

a₄ − a₃ = 73 − 49 = 24

i.e., a_k+1 − a_k is same every time.

Therefore, the given numbers are in A.P.

And, d = 24

Three more terms are

a₅ = 73 + 24 = 97

a₆ = 97 + 24 = 121

a₇ = 121 + 24 = 145