SSC CGL Model Paper 2

Let a be the first term and d be the common difference of an A.P.
${\mathit{A}}_7=-15$ and ${\mathit{A}}_{12}=5$ (Given)
Then, $-15=\mathit{a}+\left(7-1\right)\mathit{d}$
$\left[\because \mathit{A}=\mathit{a}+\left(\mathit{n}-1\right)\mathit{d}\right]$
$-15=\mathit{a}+6\mathit{d}$ ...(i)
$-5=\mathit{a}+\left(12-1\right)\mathit{d}$
⇒ $5=\mathit{a}+11\mathit{d}$ ...(ii)
Subtracting Eq. (ii) from Eq. (i),
⇒ $20=5\mathit{d}$
∴ $\mathit{d}=\frac{20}{5}=4$
Putting d = 4 in Eq. (i),
$-15=\mathit{a}+6\mathit{d}$
⇒ $-15=\mathit{a}+6\times 4$
⇒ $-15=\mathit{a}+24$
⇒ $\mathit{a}=-24-15=-39$
∴ ${\mathit{A}}_{16}=\mathit{a}+\left(16-1\right)\mathit{d}$
⇒ ${\mathit{A}}_{16}=-39+15\times 4$
⇒ ${\mathit{A}}_{16}=-39+60$
∴ ${\mathit{A}}_{16}=21$