If $b + c, c + a, a + b$ are in A.P then Prove that $a, b, c$ are also in A.P.

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Solution

$b + c, c + a, c + b$ are in A.P
$∴ 2 (c + a) = b + c + a + b$
$\Rightarrow 2 c + 2 a = a + 2 b + c$
$\Rightarrow a + c = 2 b$
$∴$ a,b,c are in A.P.

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