Q7 of 110 Page 58

A geometric series consists of four terms and has a positive common ratio. The sum of the first two terms is 9 and sum of the last two terms is 36. Find the series.

Let the first term = a


And common ratio = r


Series : a, ar, ar2, ar3


⇒ a + ar = 9


⇒ a(1 + r) = 9 ………………(1)


⇒ ar2 + ar3 = 36


⇒ ar2(1 + r) = 36


⇒ 9r2 = 36 ( From Equation (1))


⇒ r2 = 4


⇒ r = 2


Putting the value of r in (1),


⇒ a(1 + 2) = 9


⇒ 3a = 9


⇒ a = 3


∴ Series : 3 + 6 + 12 + 24


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