Which of the following are APs? If they form an AP, find the common difference $d$ and write three more terms.
$a, a^2, a^3, a^4, …….$

Given:

Given sequence is $a, a^2, a^3, a^4, …….$

To do:

We have to check whether the given sequence is an AP. If it is an AP we have to find the common difference $d$ and write three more terms.

Solution:

In the given sequence,

$a_1=a, a_2=a^2, a_3=a^3$

$a_2-a_1=a^2-a=a(a-1)$

$a_3-a_2=a^3-a^2=a^2(a-1)$

$a_2 - a_1 ≠ a_3 - a_2$

Therefore, the given sequence is not an AP.

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Updated on: 10-Oct-2022

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