Let a1, a2, a3,...... be an A. P. with a 6 = 2. Then the common difference of this A. P., which maximises the produce a1a4a5, is :

Question

Let a1, a2, a3,...... be an A. P. with a 6 = 2. Then the common difference of this A. P., which maximises the produce a1a4a5, is : (A) (6/5) (B) (8/5) (C) (2/3) (D) (3/2)

Tardigrade Admin · Accepted Answer

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'(d) = 0 ⇒ d = (2/3) , (8/5) f"(d) <0 at d = 8/5 ⇒ d = (8/5)

Q. 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 :

$\frac{6}{5}$

$\frac{8}{5}$

$\frac{2}{3}$

$\frac{3}{2}$

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

Q. Let a1​,a2​,a3​,...... be an A.P. with a 6=2. Then the common difference of this A.P., which maximises the produce a1​a4​a5​, is :

56​

58​

32​

23​