Question

If the first term of a G.P., $a_1,a_2,a_3,..$ is unity, then the value of $4a_2+5a_3$ will be minimum when the common ratio is

• A. $\frac{1}{3}$
• B. $-\frac{1}{3}$
• C. $\frac{2}{5}$
• D. $-\frac{2}{5}$

Answer 1

The correct option is D $-\frac{2}{5}$

Let $r$ be the common ratio
$a_1=1$, then $a_2=r,a_3=r^2$
$\therefore 4a_2+5a_3=4r+5r^2$ is minimum when $r=-\frac{4}{2\times 5}=-\frac{2}{5}$
$(a>0,a{x}^2+bx+c\text{is minimum at}x=-\frac{b}{2a})$