Match the AP’s given in column A with suitable common differences given in column B.
A, $2,-2,-6,-10, \ldots$
Here, common difference. $d=-2-2=-4$
$A_{2} . \because$ $a_{t,} a+(n-1) d$
$\Rightarrow$ $0=-18+(10-1) d$
$18=9 d$
$\therefore$ Common difference, $d=2$
$A_{3} \cdot \because \quad a_{10}=6$
$\Rightarrow \quad a+(10-1) d=6$
$\Rightarrow \quad 0+9 d=6$ $[\because a=0$ (given) $]$
$9 d=6 \Rightarrow d=\frac{2}{3}$
$A_{4} \because \quad a_{2}=13$
$\Rightarrow \quad a+(2-1) d=13 \quad\left[\because a_{n}=a+(n-1) d\right]$
$\Rightarrow \quad a+d=13 \quad \ldots(i)$
and $\quad a_{4}=3 \Rightarrow a+(4-1) d=3$
$\therefore \quad a+3 d=3$ ....(ii)
On subtracting Eq. (i) from Eq. (ii), we get
$2 d=-10$
$\Rightarrow \quad d=-5$
$\therefore \quad\left(A_{1}\right) \rightarrow B_{4},\left(A_{2}\right) \rightarrow B_{51}\left(A_{3}\right) \rightarrow B_{1}$ and $\left(A_{4}\right) \rightarrow B_{2}$