Q6 of 8 Page 180

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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