Which of the following are APs? If they form an AP, find the common difference $d$ and write three more terms.
$\sqrt2, \sqrt8, \sqrt{18}, \sqrt{32}, …..$

Given:

Given sequence is $\sqrt2, \sqrt8, \sqrt{18}, \sqrt{32}, …..$

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:

$\sqrt8=2\sqrt2$

$\sqrt{18}=3\sqrt2$

$\sqrt{32}=4\sqrt2$

Given sequence can be written as $\sqrt2, 2\sqrt2, 3\sqrt{2}, 4\sqrt{2}, …..$

In the given sequence,

$a_1=\sqrt2, a_2=2\sqrt2, a_3=3\sqrt2$

$a_2-a_1=2\sqrt2-\sqrt2=\sqrt2$

$a_3-a_2=3\sqrt2-2\sqrt2=\sqrt2$

$a_2 - a_1 = a_3 - a_2$

$d=a_2 - a_1=\sqrt2$

$a_5=a_4+d=4\sqrt2+ \sqrt2=5\sqrt2$

$a_6=a_5+d=5\sqrt2 + \sqrt2=6\sqrt2$

$a_7=a_6+d=6\sqrt2+ \sqrt2=7\sqrt2$

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Updated on: 10-Oct-2022

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