SSC CGL 17 Aug 2017 Shift 1 Paper

Let a be the first term and d be the common difference of an A.P.
Then, according to the question,
${\mathit{A}}_3=\mathit{a}+\left(3-1\right)\mathit{d}$
⇒ $-8=\mathit{a}+2\mathit{d}$ ...(i)
and ${\mathit{A}}_9=\mathit{a}+\left(9-1\right)\mathit{d}$
⇒ $10=\mathit{a}+8\mathit{d}$ ... (ii)
On solving Eqs. (i) and (ii),
$\mathit{a}=-14$ and $\mathit{d}=3$
∴ ${\mathit{A}}_{16}=\mathit{a}+\left(16-1\right)\mathit{d}$
$=-14+\left(15\right)\times 3$
$=-14+45=31$