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JEE Main201912 Apr 2019Morning ShiftMathematicsSequences and SeriesActual

Let S n denote the sum of the first n terms of an A . P . . If S 4 = 16 and S 6 = - 48 , then S 10 is equal to:

Options

  1. A- 320
  2. B- 380
  3. C- 260
  4. D- 410

Correct answer

A. - 320

Step-by-step solution

Let the first term of A . P . is ‘ a ’ and the common difference is ‘ d ’ . ∴   S 4 = 4 2 2 a + 4 - 1 d = 16 ⇒ 2 a + 3 d = 8       . . . i and S 6 = 6 2 2 a + 6 - 1 d = - 48 ⇒ 2 a + 5 d = - 16         . . . i i ∴ From ( i )   &   ( i i ) , a = 22 & d = - 12 ∴   S 10 = 10 2 ( 2 a + 9 d ) = 5 2 × 22 + 9 - 12 = - 320

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