Progression (Sequence and Series)Medium
Question
If the sum of the first 2n terms of the 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
Options
A.10
B.12
C.11
D.13
Solution
According to given condition,
S2n = Sn
⇒
[2 × 2 + (2n - 1) × 3] = 
[2 × 57 + (n - 1) × - 2]
⇒ (4 + 6n - 3) =
(114 + 2n - 2)
⇒ 6n + 1 = 57 + n - 1
⇒ 5n = 55
⇒ n = 11.
S2n = Sn
⇒
[2 × 2 + (2n - 1) × 3] = [2 × 57 + (n - 1) × - 2]⇒ (4 + 6n - 3) =
(114 + 2n - 2)⇒ 6n + 1 = 57 + n - 1
⇒ 5n = 55
⇒ n = 11.
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