Answer :

Since a, b, c are in AP

⇒ 2b = a + c

When 3^{a}, 3^{b}, 3^{c} are in GP

⇒ 3^{2b} = 3^{a} × 3^{c}

⇒ 3^{2b} = 3^{a + c}

⇒ 2b = a + b

Which is true iff a, b, c are in AP.

Hence, Proved.

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