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…

Let Sn denote the sum of the first n terms of an A.P.. If S4=16 and S6=-48 , then S10 is equal to:
  1. -320
  2. -380
  3. -260
  4. -410

Solution

Let the first term of A.P. is ‘a’ and the common difference is ‘d’.
∴ S4=422a+4-1d=16
⇒2a+3d=8   ...i
and S6=622a+6-1d=-48
⇒2a+5d=-16    ...ii
∴ From (i) & (ii), a=22 & d=-12
∴ S10=102(2a+9d)=52×22+9-12
=-320

Asked in: JEE Main 2019 (12 Apr Shift 1)

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