Which of the following form an AP? Justify your answer.
$ \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \ldots $

Given:

Given sequence is \( \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \ldots \)

To do:

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

Solution:

In the given sequence,

$a_1=\frac{1}{2}, a_2=\frac{1}{3}, a_3=\frac{1}{4}$

$a_2-a_1=\frac{1}{3}-\frac{1}{2}=\frac{2-3}{6}=\frac{-1}{6}$

$a_3-a_2=\frac{1}{4}-\frac{1}{3}=\frac{3-4}{12}=\frac{-1}{12}$

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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