SATHEE: Sequences and Series 2 Question 9

Sequences and Series 2 Question 9

10.

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

(2001, 1M)

(a) 10

(b) 12

(d) 13

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Answer:

Correct Answer: 10. (c)

Solution:

According to given condition,

$S_{2 n} = S_{n}^{'}$

$\Rightarrow \frac{2 n}{2} [2 \times 2 + (2 n - 1) \times 3]$

$= \frac{n}{2} [2 \times 57 + (n - 1) \times 2]$

$\Rightarrow (4 + 6 n - 3) = \frac{1}{2} (114 + 2 n - 2)$

$\Rightarrow 6 n + 1 = 57 + n - 1 \Rightarrow$

$∴ n = 11$

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Sequences and Series 2 Question 9

10.

Answer:

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