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प्रश्न
If a, b, c is in A.P. then show that 3a, 3b, 3c is in G.P.
उत्तर
If a, b, c are in A.P
t2 – t1 = t3 – t2
b – a = c – b
2b = c + a
To prove that 3a, 3b, 3c is in G.P
⇒ 32b = 3c+a + a ...[Raising the power both sides]
⇒ 3b. 3b = 3c. 3a
⇒ `(3^"b")/(3^"a") = (3^"c")/(3^"b")`
⇒ `("t"_2)/("t"_1) = ("t"_3)/("t"_1)`
⇒ Common ratio is same for 3a, 3b, 3c
⇒ 3a, 3b, 3c forms a G.P
∴ Hence it is proved.
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