Column AColumn B($A_{1}$) $2">

Match the APs given in column A with suitable common differences given in column B.
Column AColumn B
($A_{1}$) $2

To do:

We have to match the APs given in column A with suitable common differences given in column B.

Solution:

($A_{1}$) $2,-2,-6,-10, \ldots$

Here,

$a_1=2, a_2=-2, a_2=3=-6$

Common difference $a_2-a_1=-2-1$

$=-3$

($A_{2}$) $a=-18, n=10, a_{n}=0$

Here,

$a_1=a=-18$

$a_10=a+(10-1)d$

$0=-18+9d$

$9d=18$

$d=\frac{18}{9}$

$d=2$

($A_{3}$) $a=0, a_{10}=6$

$a_{10}=a+(10-1)d$

$6=0+9d$

$9d=6$

$d=\frac{6}{9}$

$d=\frac{2}{3}$

($A_{4}$) $a_2=13, a_{4}=3$

$a_4=a+(4-1)d$

$3=a+3d$.......(i)

$a_2=a+(2-1)d$

$13=a+d$......(ii)

Subtracting (ii) from (i), we get,

$3-13=a+3d-a-d$

$-10=2d$

$d=\frac{-10}{2}$

$d=-5$

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Updated on: 10-Oct-2022

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