Question

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

Column A Column B
A. $-2,2,6,10,...$ 1. $\frac{2}{3}$
B. $a=18,n=10,a_n=0$ 2. $-5$
C. $a=0,a_{10}=6$ 3. $4$
D. $a_2=13,a_4=3$ 4. $-4$
5. $-2$
6. $\frac{1}{2}$
7. $5$

• A. A-3, B-5, C-1, D-2
• B. A-4, B-1, C-3, D-2
• C. A-2, B-7, C- 5, D-6
• D. A-7, B-4, C-2, D- 2

Answer 1

Answer: (A)

A-3, B-5, C-1, D-2

Given,$A:-2,2,6,\mathrm{10...}$
Clearly, it is an AP with first term $a=-2$ and common difference $d=6-2=4$
$\therefore A\to 3$
Given, $B:a=18,n=10,a_n=0$
Now, $a_n=a+(n-1)d=0$
$\Rightarrow 9d=-18\Rightarrow d=-2$

$\therefore B\to 5$
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
$2d=-10\Rightarrow d=-5$
$\therefore D\to 2$