If a, b and c are in a G.P then $a + b, 2 b, b + c$ are in

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none of these

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Solution

The correct option is A AP
If a,b,c are in GP, then $b^{2} = a c b = \sqrt{c a}$

If a+b, 2b, b+c are in AP, then 4b = a+ 2b+c
Or
$4 \sqrt{c a} = a + c + 2 \sqrt{a c} 2 \sqrt{a c} = a + c$
Hence, a,b,and c are in AP.

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