If a, b, c are in A.P. then show that 3a, 3b, 3c are in G.P.

If a, b, c are in A.P. then show that 3a, 3b, 3c are in G.P.
Solution :
If a, b, c are in A.P, then b = (a + c)/2
In G.P,  b = √ac
To prove that 3a, 3b, 3c are in G.P.
3b  = √(3a 3c
3b  = (3a + c)1/2
3b  = 3(a+c)/2
b = (a + c)/2
Hence 3a, 3b, 3c are in G.P.

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