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 $a_1a_4a_5$, is :

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

Answer 1

Answer: (B)

Let $a$ is first term and d is common difference then, $a + 5d = 2$ (given) ...(1)
f(d) = (2 - 5d) (2 - 2d) (2 - d)
$f'\left(d\right) = 0 \Rightarrow d = \frac{2}{3} , \frac{8}{5} $
$f"\left(d\right) <0$ at $ d = 8/5$
$\Rightarrow d = \frac{8}{5} $