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Let 2 nd , 8 th and 44 th , terms of a non-constant A . P . be respectively the 1 st , 2 nd and 3 rd terms of G . P . If the first term of A.P. is 1 then the sum of first 20 terms is equal to-

Options

  1. A980
  2. B960
  3. C990
  4. D970

Correct answer

D. 970

Step-by-step solution

Given: 2 nd , 8 th , 44 th terms of A . P are 1 st , 2 nd & 3 rd terms respectively of G . P . And first term of A . P . is 1 and let d be common difference So, 1 + d , 1 + 7 d , 1 + 43 d are 1 s t , 2 n d & 3 r d term of G . P . ⇒ 1 + 7 d 1 + d = 1 + 43 d 1 + 7 d ⇒ 1 + 7 d 2 = 1 + 43 d 1 + d ⇒ 1 + 49 d 2 + 14 d = 1 + 43 d 2 + 44 d ⇒ 6 d 2 = 30 d ⇒ d = 5 Now finding the sum of first 20 terms of AP, ⇒ S 20 = 10 2 × 1 + 19 × 5 ⇒ S 20 = 970

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