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Maths-

General

Easy

Question

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

10
12
11
13

The correct answer is: 11

Given,
$2 plus 5 plus 8 plus...2 n$ terms $equals 57 plus 59 plus 61 plus... n$ terms
$rightwards double arrow fraction numerator 2 n over denominator 2 end fraction open square brackets 4 open parentheses 2 n minus 1 close parentheses 3 close square brackets equals fraction numerator n over denominator 2 end fraction open square brackets 114 plus open parentheses n minus 1 close parentheses 2 close square brackets$
$rightwards double arrow 6 n plus 1 equals n plus 56$
$rightwards double arrow 5 n equals 55$
$rightwards double arrow n equals 11$

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