Mathematics · Sequence and Series

JEE Main 2024 — 29 January, Shift 1 — Question 2

In an A.P., the sixth terms $\mathrm{a}_{6}=2$ . If the $a_{1} a_{4} a_{5}$ is the greatest, then the common difference of the A.P., is equal to

Answer: B

$\mathrm{a}_{6}=2 \Rightarrow \mathrm{a}+5 \mathrm{~d}=2$

$\mathrm{a}_{1} \mathrm{a}_{4} \mathrm{a}_{5}=\mathrm{a}(\mathrm{a}+3 \mathrm{~d})(\mathrm{a}+4 \mathrm{~d})$

$=(2-5 \mathrm{~d})(2-2 \mathrm{~d})(2-\mathrm{d})$

$f(d)=8-32 d+34 d^{2}-20 d+30 d^{2}-10 d^{3}$

$f^{\prime}(d)=-2(5 d-8)(3 d-2)$

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

Answer key and solution verified before publishing.

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