If sum of first 2n terms of 2,,5,,8... is equal to sum of first n terms of 57,,59,,61... , then n is

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8. Sequences and Series

easy

If the sum of the first $2n$ terms of $2,\,5,\,8...$ is equal to the sum of the first $n$ terms of $57,\,59,\,61...$, then $n$ is equal to

A

$10$

B

$12$

C

$11$

D

$13$

(IIT-2001)

Solution

(c) Given, $\frac{{2n}}{2}\{ 2.2 + (2n – 1)3\} = \frac{n}{2}\{ 2.57 + (n – 1)2\} $

or $2(6n + 1) = 112 + 2n$ or $10n = 110,\,\,\,\,\,$

$\therefore n = 11$.

Standard 11

Mathematics

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