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Question
Answer the following:
Which 2 terms are inserted between 5 and 40 so that the resulting sequence is G.P.
Solution
Let the required numbers be G1 and G2.
∴ 5, G1, G2, 40 are in G.P.
∴ t1 = 5, t2 = G1, t3 = G2, t4 = 40
∴ t1 = a = 5, t4 = 40
tn = arn–1
∴ t4 = 5(r)4–1
∴ 40 = 5r3
∴ r3 = 8 = 23
∴ r = 2
G1 = t2 = ar = 5 (2) = 10
G2 = t3 = ar2 = 5(2)2 = 20
∴ For resulting sequence to be in G.P. we need to insert numbers 10 and 20.
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