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Question
Insert two numbers between 1 and −27 so that the resulting sequence is a G.P.
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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
∴ For resulting sequence to be G.P. we need to insert numbers −3 and 9.
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