Let a1, a2, a3,......be an A.P.

Question

Let a1, a2, a3,......be an A.P. with a6 = 2. Then the common difference of this A.P., which maximises the
product a1a4a5, is :

Accepted Answer

first term = a, Common difference = d

$$ \therefore $$  a + 5d = 2

a1. a4. a5 = a(a + 3d) (a + 4d)

f(d) = (2 -- 5d) (2 -- 2d) (2 -- d)

$$ \Rightarrow $$ $$f'(d) = 0 \Rightarrow d = {2 \over 3},{8 \over 5}$$

$$ \Rightarrow $$ $$f''(d) < 0\,at\,d = {8 \over 5}$$

$$\, \Rightarrow d = {8 \over 5}$$

Solutions · 1