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Q.

The sum of infinite terms of a decreasing G.P. is equal to the greatest value of the function 

f(x) = x3+3x–9 in the interval [–2, 3] and the difference between the first two terms is f1(0). The common ratio of the G.P. is

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a

1/3

b

2/3

c

–2/3

d

4/3

answer is B.

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Detailed Solution

f(3) = 27 ⇒ S = 27 ⇒ f1(x) = 3x2 + 3
⇒f1(0)=3⇒a−ar=3⇒a(1−r)=3a(1−r)×a1−r=81⇒a2=81,a=9⇒1−r=13⇒r=2/3S=91−r=27

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