In an A.P., the sixth term a_6=2.

Question

In an A.P., the sixth term $a_6=2$. If the product $a_1 a_4 a_5$ is the greatest, then the common difference of the A.P. is equal to

Accepted Answer

$$\begin{aligned}
& a_6=2 \Rightarrow a+5 d=2 \
& a_1 a_4 a_5=a(a+3 d)(a+4 d) \
& =(2-5 d)(2-2 d)(2-d) \
& f(d)=8-32 d+34 d^2-20 d+30 d^2-10 d^3 \
& f^{\prime}(d)=-2(5 d-8)(3 d-2)
\end{aligned}$$

$$\mathrm{d}=\frac{8}{5}$$

Solutions · 1