Sequences and Series 2 Question 9
10.
If the sum of the first $2 n$ terms of the AP series $2,5,8, \ldots$, is equal to the sum of the first $n$ terms of the AP series $57,59,61, \ldots$, then $n$ equals
(2001, 1M)
(a) 10
(b) 12
(c) 11
(d) 13
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Answer:
Correct Answer: 10. (c)
Solution:
- According to given condition,
$S _{2 n} =S _n^{\prime} $
$\Rightarrow \frac{2 n}{2}[2 \times 2+(2 n-1) \times 3] $
$=\frac{n}{2}[2 \times 57+(n-1) \times 2] $
$\Rightarrow (4+6 n-3) =\frac{1}{2}(114+2 n-2)$
$\Rightarrow 6 n+1=57+n-1 \Rightarrow $
$\therefore n=11$
