8^{th} term of series 2√ 2 + √ 2 + 0 + ..... will be

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8. Sequences and Series

easy

$8^{th}$ term of the series $2\sqrt 2 + \sqrt 2 + 0 + .....$ will be

A

$ - 5\sqrt 2 $

B

$5\sqrt 2 $

C

$10\sqrt 2 $

D

$ - 10\sqrt 2 $

Solution

(a) Obviously the given series $2\sqrt 2 + \sqrt 2 + 0 + …….$ is an $A.P.$

Here $a = 2\sqrt 2 ,\;d = – \sqrt 2 $.

Hence ${8^{th}}$ term of the series

$ = 2\sqrt 2 + (8 – 1)( – \sqrt 2 ) = – 5\sqrt 2 $.

Standard 11

Mathematics

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(JEE MAIN-2013)