7^ th term of the sequence 2 , ;10 , ;5 2 , ;....... is - Vidyadip

MCQ

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

A
$125\sqrt {10} $
B
$25\sqrt 2 $
C
$125$
✓
$125\sqrt 2 $

✓

Answer

Correct option: D.

$125\sqrt 2 $

d
(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 $.

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