Which of the following form an AP? Justify your answer.
$ 2,2^{2}, 2^{3}, 2^{4}, \ldots $

Academic Mathematics NCERT Class 10

Given:

Given sequence is \( 2,2^{2}, 2^{3}, 2^{4}, \ldots \)

To do:

We have to check whether the given sequence is an AP.

Solution:

In the given sequence,

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

$a_2-a_1=2^2-2=4-2=2$

$a_3-a_2=2^3-2^2=8-4=4$

Here,

$a_2 - a_1 ≠ a_3 - a_2$

Therefore, the given sequence is not an AP.

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Updated on: 10-Oct-2022

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