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JEE Main202125 Jul 2021Morning ShiftMathematicsSequences and SeriesActual

Let S n be the sum of the first n terms of an arithmetic progression. If S 3 n = 3 S 2 n , then the value of S 4 n S 2 n is :

Options

  1. A6
  2. B4
  3. C2
  4. D8

Correct answer

A. 6

Step-by-step solution

Let a be first term and d be common difference of this A.P. Given S 3 n = 3 S 2 n ⇒ 3 n 2 2 a + 3 n - 1 d = 3 × 2 n 2 2 a + 2 n - 1 d ⇒ 2 a + ( 3 n - 1 ) d = 4 a + ( 4 n - 2 ) d ⇒ 2 a + ( n - 1 ) d = 0 Now S 4 n S 2 n = 4 n 2 2 a + 4 n - 1 d 2 n 2 2 a + 2 n - 1 d = 2 2 a + n - 1 d + 3 n d 2 a + n - 1 d + n d = 6 n d n d = 6

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