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Match the APs given in column A with suitable common differences given in column B.
Column A | Column 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, $3-13=a+3d-a-d$ $-10=2d$ $d=\frac{-10}{2}$ $d=-5$ Advertisements
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