{7^{th}} term of sequence √ 2 ,√ {10} ,5√ 2 ,....... is

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8. Sequences and Series

easy

${7^{th}}$ term of the sequence $\sqrt 2 ,\;\sqrt {10} ,\;5\sqrt 2 ,\;.......$ is

A

$125\sqrt {10} $

B

$25\sqrt 2 $

C

$125$

D

$125\sqrt 2 $

Solution

(d) Given sequence is $\sqrt 2 ,\;\sqrt {10} ,\;\sqrt {50} ……..$

Common ratio $r = \sqrt 5 $,

first term $a = \sqrt 2 $, then ${7^{th}}$ term

${t_7} = \sqrt 2 {(\sqrt 5 )^{7 – 1}} = \sqrt 2 {(\sqrt 5 )^6}$

$= \sqrt 2 {(5)^3} = 125\sqrt 2 $.

Standard 11

Mathematics

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