For  an increasing  AP ${\mathrm{a}}_1,{\mathrm{a}}_2,\dots ,{\mathrm{a}}_{\mathrm{n}}$ if ${\mathrm{a}}_1+{\mathrm{a}}_3+{\mathrm{a}}_5=-12$  and ${\mathrm{a}}_1{\mathrm{a}}_3{\mathrm{a}}_5=80$ then which of the  following is/are  true?

${\mathrm{a}}_1+{\mathrm{a}}_3+{\mathrm{a}}_5=-12$ , $\mathrm{a}+\mathrm{a}+2\mathrm{d}+\mathrm{a}+4\mathrm{d}=-12(\mathrm{d}>0)$

$\mathrm{a}+2\mathrm{d}=-4$        ……..(i)

$\begin{array}{l}{\mathrm{a}}_1{\mathrm{a}}_3{\mathrm{a}}_5=80\\ \mathrm{a}(\mathrm{a}+2\mathrm{d})(\mathrm{a}+4\mathrm{d})=80\end{array}$

or $\mathrm{a}(-4)(-4-2\mathrm{d}+4\mathrm{d})=80$     [from Eq(i)]

or $(-4-2\mathrm{d})(-4+2\mathrm{d})=-20\Rightarrow \mathrm{d}=\pm 3$

Since, AP is increasing, so d = $+3;\mathrm{a}=-10$

Hence, $\left.\begin{array}{l}{\mathrm{a}}_1=-10;{\mathrm{a}}_2=-7\\ {\mathrm{a}}_3=\mathrm{a}+2\mathrm{d}=-10+6=-4\\ {\mathrm{a}}_5=\mathrm{a}+4\mathrm{d}=-10+8=-2\end{array}\right\}$