Question:
Let $\mathrm{a}_{1}, \mathrm{a}_{2}, \mathrm{a}_{3}, \ldots . .$ be an A. P. with $\mathrm{a}_{6}=2$. Then the common difference of this A. P., which maximises the produce $\mathrm{a}_{1} \mathrm{a}_{4} \mathrm{a}_{5}$, is :
Correct Option: , 2
Solution:
Let a is first term and $\mathrm{d}$ is common difference then, a $+5 \mathrm{~d}=2$ (given) ...(1)
$f(d)=(2-5 d)(2-2 d)(2-d)$
$\mathrm{f}^{\prime}(\mathrm{d})=0 \quad \Rightarrow \mathrm{d}=\frac{2}{3}, \frac{8}{5}$
$\mathrm{f}^{\prime \prime}(\mathrm{d})<0$ at $\mathrm{d}=8 / 5$
$\Rightarrow \mathrm{d}=\frac{8}{5}$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.