Q4 of 8 Page 180

In a set of four numbers, the first three are in G.P. and the last three are in A.P. with a common difference of 6. If the first number is the same as the fourth, find the four numbers.

ATQ, last three numbers are in A.P with common difference = 6, let the four terms be a, a – 12, a – 6, a


Also first three numbers are in G.P. Therefore, a, ar ( = a – 12), ar2( = a – 6) and a


(a – 12)2 = a (a – 6) [Property of Geometric mean]


a2 + 144 – 24a = a2 – 6a


– 24 a + 6 a = – 144


– 18 a = – 144


⇒ a = 8


So, four terms become 8, – 4, 2, 8


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