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Paragraph: The product of 5 consecutive terms of an AP is 229635. The first, second and fifth terms are in GP. Question: What is the common difference?

Options

  1. A3
  2. B4
  3. C5
  4. D6

Correct answer

D. 6

Step-by-step solution

Let the required terms of the given AP are- a -2 ~d , a - d , a , a + d , a +2 ~d . According to the question, aligned & (a-2 d)(a-d) a(a+d)(a+2 d)=229635 & a (a^2-d^2 ) (a^2-4 d^2 )=229635 ....(i) & a-2 d, a-d, a+2 d are in G.P. & (a-d)^2=(a-2 d)(a+2 d) & (a-d)^2=a^2-4 d^2 & 5 d^2-2 a d=0 d(5 d-2 a)=0 5 d=2 a aligned ....(ii) Solving equation (i) and (ii), we have, d =6 .

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