Question

Let $a_1,a_2,a_3....$ be an A.P with $a_6=2$. Then the common difference of this A.P., which maximises the produce $a_1{a}_4{a}_5$ is:

• A. $\frac{6}{5}$
• B. $\frac{8}{5}$
• C. $\frac{2}{3}$
• D. $\frac{3}{2}$

Answer 1

The correct option is B $\frac{8}{5}$

Let $a$ is first term and $d$ is common difference then, $a+5d=\mathrm{2.....}\left(1\right)$
$f\left(d\right)=(2-5d)(2-2d)(2-d);f^{\prime }\left(d\right)=0\Rightarrow d=\frac{2}{3},\frac{8}{5}$
$f^{\prime }\left(d\right)<0\Rightarrow d=\frac{8}{5}$