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Question

If a, b and c are in A.P. and also in G.P., show that : a = b = c .

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Solution

Given : a, b, c are in A.P.

⇒ 2b = a + c .......(1)

(2b)2=(a+c)2

4b2=a2+c2+2ac ....(2)

Also,

a, b, c are in G.P.

b2=ac ......(3)

Fron (2) and (3) we get

4ac=a2+c2+2ac

a2+c2+2ac4ac = 0

a2+c22ac=0

(ac)2 = 0

⇒ a - c = 0

⇒ a = c ....(4)

From (1) and (4) we get

2b = a + a = c + c

⇒ 2b = 2a = 2c

⇒ a = b = c


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