Question

The sum of the terms of an infinitely decreasing GP is equal to the greatest value of the function f(x) = x³ + 3x - 9 on the interval [-4, 3] and the difference between the first and second terms is f′ (0). Find the value of 27r where r is the common ratio.

Answer 1

f is increasing. So, its greatest value is f(3) = 27.

Let the GP be a, ar, ar²,… with - 1 < r < 1.

a/1 - r = 27 and a - ar = 3

r = 4/3 or  r = 2/3

But, -1 < r < 1