Question

The sum of terms of infinitely decreasing GP is equal to the greatest value of the function $f\left(x\right)=x^2+3x-9$ in the interval. $[-5,3]$, & the difference between the first & second terms is f(0). Then common ratio of GP is

• A. $\frac{4}{3}$
• B. $\frac{3}{2}$
• C. $\frac{3}{5}$
• D. $\frac{2}{3}$

Answer 1

The correct option is A $\frac{4}{3}$

The function $f\left(x\right)=x^3+3x-9$ is an increasing function

$\because f^{\prime }\left(x\right)=3x^2+3>0\forall [-2,3]$

$\therefore$ Maximum value $=27$

Thus, $\frac{a}{1-r}=27$ and $a-ar=3$

$\Rightarrow a=\frac{3}{1-r}$

$\therefore {\left(\frac{1}{1-r}\right)}^2=9$

$\Rightarrow \frac{1}{1-r}=\pm 3$

$\Rightarrow 1-r=\pm \frac{1}{3}$

$\Rightarrow r=\frac{2}{3}$

$r\ne \frac{4}{3}$ as decreasing GP.