Question

Question 4 (xi)
Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.
(xi) $a,a^2,a^3,a^4,\dots$

Answer 1

If the difference between any two consecutive terms of a series is a constant value, then the series is an A.P.

Given, the series is :
$a,a^2,a^3,a^4,\dots$
Here,
$a_2-a_1=a^2-a=(a-1)a_3-a_2=a^3-a^2=a^2(a-1)a_4-a_3=a^4-a^3=a^3(a-1)$

Note that the difference between any two consecutive terms of the series is not a constant value.
Hence, the given series is not an AP.