JEE MAIN - Mathematics (2024 - 29th January Morning Shift - No. 7)
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
$$\frac{2}{3}$$
$$\frac{5}{8}$$
$$\frac{3}{2}$$
$$\frac{8}{5}$$
Explanation
$$\begin{aligned} & a_6=2 \Rightarrow a+5 d=2 \\ & a_1 a_4 a_5=a(a+3 d)(a+4 d) \\ & =(2-5 d)(2-2 d)(2-d) \\ & f(d)=8-32 d+34 d^2-20 d+30 d^2-10 d^3 \\ & f^{\prime}(d)=-2(5 d-8)(3 d-2) \end{aligned}$$
_29th_January_Morning_Shift_en_7_1.png)
$$\mathrm{d}=\frac{8}{5}$$
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