Question

Match the APs given in column A with suitable common differences given in column B.

Answer 1

Given,$A:2,6,\mathrm{10...}$
Clearly, it is an AP with first term $a=2$ and common difference $d=6-2=4$
$\therefore A\to 4$
Given, $B:a=18,n=10,a_n=0$
Now, $a_n=a+(n-1)d=0$
$\Rightarrow 9d=-18\Rightarrow d=-2$

$\therefore B\to -2$
Given, $C:a=0,a_{10}=6$
$\Rightarrow a+9d=6\Rightarrow d=\frac{6}{9}\Rightarrow d=\frac{2}{3}$
$\therefore C\to 1$
Given, $D:a_2=13,a_4=3$
$\Rightarrow a+d=13$ ...(i)
$\Rightarrow a+3d=3$ ...(ii)
On subtracting (i) from (ii), we get
$2d=-10\Rightarrow d=-5$
$\therefore D\to 2$