If sum of the first 2$n$ terms of an AP series 2, 5, 8,… is equal to the sum of the first $n$ terms of the AP series 57, 59, 61,…, then $n$ equals

Question

Dr. Abubacker · Accepted Answer

(c)
According to the given condition,
$S_{2n} = S_{n}$
$\Rightarrow \frac{2n}{2}\lbrack 2 	imes 2 + (2n - 1) 	imes 3 = \frac{n}{2}\lbrack 2 	imes 57 + (n - 1) 	imes 2brack$
$\Rightarrow (4 + 6n - 3) = \frac{1}{2}(114 + 2n - 2)$
$\Rightarrow 6n + 1 = 57 + n - 1$
$\Rightarrow 5n = 55$
$\Rightarrow n = 11$

Q. If sum of the first 2$n$ terms of an AP series 2, 5, 8,… is equal to the sum of the first $n$ terms of the AP series 57, 59, 61,…, then $n$ equals

Explanation

Reviewed by Dr. Abubacker

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