Question

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

a, a², a³, a⁴ …

Answer 1

a, a², a³, a⁴ …

It can be observed that

a₂ − a₁ = a² − a = a (a − 1)

a₃ − a₂ = a³ − a² = a² (a − 1)

a₄ − a₃ = a⁴ − a³ = a³ (a − 1)

i.e., a_k+1 − a_k is not the same every time.

Therefore, the given numbers are not in A.P.