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JEE Main20199 Jan 2019Evening ShiftMathematicsSequences and SeriesActual

Let a , b and c be the 7 t h , 11 t h and 13 t h terms respectively of a non-constant A.P. . If these are also the three consecutive terms of a G.P. , then a c is equal to:

Options

  1. A2
  2. B7 13
  3. C1 2
  4. D4

Correct answer

D. 4

Step-by-step solution

Let the first terms of A.P. be A and common difference be d , then a = A + 6 d b = A + 10 d c = A + 12 d Given a ,   b ,   c are in G. P. ⇒ b 2 = a c ⇒ A + 10 d 2 = A + 6 d A + 12 d ⇒ A 2 + 100 d 2 + 20 A d = A 2 + 18 A d + 72 d 2 ⇒ A = - 14 d Now a c = A + 6 d A + 12 d = - 14 d + 6 d - 14 d + 12 d = - 8 d - 2 d = 4

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