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If the sum of the first ten terms of the series 1 3 5 2 + 2 2 5 2 + 3 1 5 2 + 4 2 + 4 4 5 2 + … . , is 16 5 m , then m is equal to

Options

  1. A100
  2. B99
  3. C102
  4. D101

Correct answer

D. 101

Step-by-step solution

8 5 2 + 12 5 2 + 16 5 2 ........ upto ten terms T n = 4 n + 4 5 2 T n = 16 n 2 + 2 n + 1 25 T n = 16 25 n 2 + 2 n + 1 S n = 16 25 ∑ n 2 + 2 n + 1 S n = 16 25   n n + 1   2 n + 1 6 + 2 n n + 1 2 + n Put n = 10   16 25 10 · 11 · 21 6 + 2 · 10 · 11 2 + 10 = 16 25   385 + 110 + 10 = 16 25 ·   505 = 16 5 · 101 Hence m = 101

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