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

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Solution

If $a, b, c$ are in $A P$
$a + c = 2 b$
we need to prove $a + b, c + a, b + c$ are in $A P$
$∴ 2 (a + c) = b + c + a + b 2 c + 2 a = 2 b + c + a a + c = 2 b ∴ p r o v e d .$

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