Mathematics - Sequence & Series Question with Solution | TestHub

Let the first term be $a$ and common difference $d$. $a_1+a_3+a_5=3a+6d=-12\Rightarrow a+2d=-4$

$a_1{a}_2{a}_3=a(a+d)(a+2d)=8\Rightarrow a(a+d)=-2\dots \text{ (ii) }$ Check: from (i) $a+d=\frac{a-4}{2}$, so $a\cdot \frac{a-4}{2}=-2\Rightarrow a^2-4a+4=0\Rightarrow a=2,d=-3$. $a_2+a_4+a_6=3a+9d=6-27=-21.$