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If  are in AP then

  1. a, b, c are in Arithmetic progression
  2. a, b, c are in Geometric Progression
  3. a2, b2, c2 are in Arithmetic progression
  4.  are in Arithmetic progression

Answer (Detailed Solution Below)

Option 3 : a2, b2, c2 are in Arithmetic progression
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Detailed Solution

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Formula used:

If a, b, c are in AP then

2b = a + c

Calculation:

Given that,

 are in AP,

⇒ 

⇒ 

⇒ 2(a + b)(b + c) = (a + c)(a + 2b + c)

⇒ 2ab + 2ac + 2b2 + 2bc = a2 + 2ab + 2ac + 2bc + c2

⇒ 2b2 = a2 + c2

Hence, a2, b2, c2 are in AP.

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