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Question: If the sum of the first 2n terms of \(2,5,8 \ldots\) is equal to the sum of the first n terms of ...

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

A

10

B

12

C

11

D

13

Answer

11

Explanation

Solution

Given,

2n2{2.2+(2n−1)3}=n2{2.57+(n−1)2}\frac { 2 n } { 2 } \{ 2.2 + ( 2 n - 1 ) 3 \} = \frac { n } { 2 } \{ 2.57 + ( n - 1 ) 2 \}

or 2(6n+1)=112+2n2 ( 6 n + 1 ) = 112 + 2 n or 10n=110,∴n=1110 n = 110 , \quad \therefore n = 11 .