# If a b c are in A.P. then prove that 3a, 3b, 3care in G.P.

Since a, b, c are in AP

2b = a + c

When 3a, 3b, 3c are in GP

32b = 3a × 3c

32b = 3a + c

2b = a + b

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

Hence, Proved.

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