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JEE Main 2019 · 12 Apr · Shift I

JEE Main 2019 Mathematics question on Sequences and Series

Let SnS_n denote the sum of the first nn terms of an AP. If S4=16S_4 = 16 and S6=−48S_6 = -48, then S10S_{10} is equal to
  1. A.
    -260
  2. B.
    -410
  3. C.
    -320
  4. D.
    -380
Show answer and solution

Correct option: C

Solution

S₄ = (4/2)[2a + 3d] = 2(2a + 3d) = 16 → 2a + 3d = 8

S₆ = (6/2)[2a + 5d] = 3(2a + 5d) = -48 → 2a + 5d = -16

Subtracting: 2d = -24 → d = -12, then 2a = 8 - 3(-12) = 44 → a = 22

S₁₀ = (10/2)[2(22) + 9(-12)] = 5[44 - 108] = 5(-64) = -320

[JEE Main 2019 · 12 Apr · Shift I]

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