Comprehension

Direction : Consider the following for the items that follow :  

The product of 5 consecutive terms of an AP is 229635. The first, second and fifth terms are in GP. 

What is the common difference?

This question was previously asked in
NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)
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  1. 3
  2. 4
  3. 5
  4. 6

Answer (Detailed Solution Below)

Option 4 : 6
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Detailed Solution

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Explanation:

Let the required terms of AP are a – 2d, a – d, a, a + d, a + 2d

⇒ (a – 2d) (a – d) a (a + d) (a + 2d) = 2,29,635

⇒ a(a 2 – d2 ) (a 2 – 4d2 ) = 2,29,635.....(i)

Now  a – 2d, a – d and a + 2d are in GP

⇒ (a – d)2 = a2 – 4d2

⇒ 5d2 – 2ad = 0 

⇒ d(5d – 2a) = 0

⇒ 5d = 2a......(ii)

Solving equation (i) and (ii), we get

⇒ d = 6

∴ Option (d) is correct.

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