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The sum of n terms of two arithmetic series are in the ratio 2n + 3 : 6n + 5, then the ratio of their 13th terms is

Options

  1. A53 : 155
  2. B27 : 87
  3. C29 : 83
  4. D31 : 89

Correct answer

A. 53 : 155

Step-by-step solution

Since, S n 1 S n 2 = 2n + 3 6n + 5 ...(i) ⇒ n 2 2a 1 + n - 1 d 1 n 2 2a 2 + n - 1 d 2 = 2n + 3 6n + 5 ⇒ a 1 + n - 1 2 d 1 a 2 + n - 1 2 d 2 = 2n + 3 6n + 5 Put n - 1 2 = 12 ⇒ n = 25 ∴ a 1 + 1 2 d 1 a 2 + 1 2 d 2 = 5 3 1 5 5 ⇒ T 1 3 1 T 1 3 2 = 5 3 1 5 5

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