Which of the following are APs? If they form an AP, find the common difference $d$ and write three more terms.
$3, 3 + \sqrt2, 3 + 2\sqrt2, 3 + 3\sqrt2, …..$

Given:

Given sequence is $3, 3 + \sqrt2, 3 + 2\sqrt2, 3 + 3\sqrt2, …..$

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,

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

$a_2-a_1=3 + \sqrt2-3=\sqrt2$

$a_3-a_2=3 + 2\sqrt2-(3 + \sqrt2)=\sqrt2$

$a_2 - a_1 = a_3 - a_2$

$d=a_2 - a_1=\sqrt2$

$a_5=a_4+d=3 + 3\sqrt2+ \sqrt2=3 + 4\sqrt2$

$a_6=a_5+d=3 + 4\sqrt2 + \sqrt2=3 + 5\sqrt2$

$a_7=a_6+d=3 + 5\sqrt2+ \sqrt2=3 + 6\sqrt2$

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Updated on: 10-Oct-2022

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