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JEE Main202430 Jan 2024Morning ShiftMathematicsSequences and SeriesActual

Let S a denote the sum of first n terms an arithmetic progression. If S 20 = 790 and S 10 = 145 , then S 15 - S 5 is :

Options

  1. A395
  2. B390
  3. C405
  4. D410

Correct answer

A. 395

Step-by-step solution

Given, In an arithmetic progression sum of first 20 terms is 790 So, let a be the first term and d be common difference, So, S 20 = 20 2 2 a + 19 d = 790 . . . . . 1 And sum of the first 10 terms is 145 So, S 10 = 10 2 2 a + 9 d = 145 . . . . . 2 By solving equation 1 & 2 we get, a = - 8 & d = 5 Then, S 15 - S 5 = 15 2 2 × - 8 + 14 × 5 - 5 2 2 × - 8 + 4 × 5 ⇒ S 15 - S 5 = 405 - 10 = 395

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