Find:18th term of the A.P. $\sqrt2, 3\sqrt2, 5\sqrt2, ……….$

Given:

Given A.P. is $\sqrt2, 3\sqrt2, 5\sqrt2, ……….$

To do:

We have to find the 18th term of the given A.P.

Solution:

Here,

$a_1=\sqrt2, a_2=3\sqrt2, a_3=5\sqrt2$

Common difference $d=a_2-a_1=3\sqrt2-\sqrt2=\sqrt2(3-1)=2\sqrt2$

We know that,

nth term $a_n=a+(n-1)d$

Therefore,

18th term $a_{18}=\sqrt2+(18-1)2\sqrt2$

$=\sqrt2+17\times2\sqrt2$

$=\sqrt2(1+34)$

$=35\sqrt2$

The 18th term of the given A.P. is $35\sqrt2$. 

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Updated on: 10-Oct-2022

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