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Manipal MET2023MathematicsSequences and Series

If a^2, b^2 and c^2 are in AP, then b+c, c+a and a+b are in

Options

  1. AAP
  2. BGP
  3. CHP
  4. DNone of these

Correct answer

C. HP

Step-by-step solution

We have, a^2, b^2 and c^2 are in AP adding a b+b c+c a to each of these terms, we get a^2+a b+b c+c a, b^2+a b+b c+c a and c^2+a b+b c+c a are in AP. (a+b)(a+c),(b+c)(b+a) and (c+a)(c+b) are in AP. Dividing each term by (b+c)(c+a)(a+b) , we get 1 b+c , 1 c+a and 1 a+b are in AP b+c, c+a and a+b are in HP.

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