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Question

The sum of infinite terms of decreasing GP is equal to the greatest value of the function f(x)=x3+3x9 in the interval [-2, 3] and the difference between the first two terms is f(0). Then the common ratio of the GP is

A
23
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B
43
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C
23
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D
43
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Solution

The correct option is D 23
The function f(x)=x3+3x9 is an increasing function
f(x)=3x2+3>0[2,3]
Maximum value =27

Thus, a1r=27 and aar=3
a=31r
(11r)2=9
11r=±3
1r=±13
r=23
r43 as decreasing GP.

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