Sequences And Series Question 9
Question 9 - 2024 (29 Jan Shift 1)
In an A.P., the sixth terms $a_{6}=2$. If the $a_{1} a_{4} a_{5}$ is the greatest, then the common difference of the A.P., is equal to
(1) $\frac{3}{2}$
(2) $\frac{8}{5}$
(3) $\frac{2}{3}$
(4) $\frac{5}{8}$
Show Answer
Answer (2)
Solution
$a_{6}=2 \Rightarrow a+5 d=2$
$a_{1} a_{4} a_{5}=a(a+3 d)(a+4 d)$
$=(2-5 d)(2-2 d)(2-d)$
$f(d)=8-32 d+34 d^{2}-20 d+30 d^{2}-10 d^{3}$
$f^{\prime}(d)=-2(5 d-8)(3 d-2)$
$\mathrm{d}=\frac{8}{5}$
