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Question
Insert two numbers between 1 and – 27 so that the resulting sequence is a G.P.
Solution
Let the required numbers be G1 and G2.
∴ 1, G1, G2, – 27 are in G.P.
∴ t1 = 1, t2 = G1, t3 = G2, t4 = – 27
∴ t1 = a = 1
tn = arn–1
∴ t4 = (1)r4–1
∴ – 27 = r3
∴ r3 = (– 3)3
∴ r = – 3
∴ G1 = t2 = ar = 1(– 3) = – 3
G2 = t3 = ar2 = 1(– 3)2 = 9
∴ – 3 and 9 are the required numbers to be inserted between 1 and – 27 so that th resulting sequence is a G.P.
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