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
Objective Question II
(One or more than one correct option)
Show Answer
Answer:
Correct Answer: 10. (c)
Solution:
- According to given condition,
$$ \begin{array}{rlrl} S _{2 n} & =S _n^{\prime} \\ \Rightarrow & \frac{2 n}{2}[2 \times 2+(2 n-1) \times 3] & =\frac{n}{2}[2 \times 57+(n-1) \times 2] \\ \Rightarrow & & (4+6 n-3) & =\frac{1}{2}(114+2 n-2) \end{array} $$
$$ \begin{array}{lc} \Rightarrow & 6 n+1=57+n-1 \Rightarrow \\ \therefore & n=11 \end{array} $$
