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

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

Column A

Column B

(A1) 2, – 2, – 6, – 10,...

(B1) \frac{2}{3}

(A2) a = –18, n = 10, an = 0

(B2) –5

(A3) a = 0, a_{10} = 6      

(B3) 4

(A4) a_2 = 13, a_4 =3  

(B4) –4
 

 (B5) 2
 

 (B6)\frac{1}{2}

 

 (B7) 5

 

Answers (1)

\\(A\textsubscript{1}) \: \: \: \: \\2, -2, -6, -10, $ \ldots $ ..\\ a\textsubscript{2}= -2, a\textsubscript{1}= 2\\ d = a\textsubscript{2} - a\textsubscript{1}\\ -2 - 2 = - 4 \: \: \: \: (B\textsubscript{4}) - 4\\ (A\textsubscript{2}) \\a = - 18, n = 10, a\textsubscript{n} = 0\\ a\textsubscript{n} = 0\\ \because a + (n - 1) d = 0\\ -18 + (10 - 1)d = 0\\ 9d = 18\\ \vspace{\baselineskip} d = 2 \: \: \: \: (B\textsubscript{5}) 2\\ (A\textsubscript{3})\\ a = 0, a\textsubscript{10} = 6\\ a + 9d = 6\\ 0 + 9d = 6\\ d=\frac{6}{9}=\frac{2}{3} \: \: \: \: (B\textsubscript{1}) 2/3\\ (A\textsubscript{4})\\ a\textsubscript{2} = 13, a\textsubscript{4} = 3\\ \because a + (n - 1) d = 0\\ a+d=13 \\ a + 3d=3 \\ - \_-\_\_\_-\_\_\_\_\_\_\\ -2d = 10\\ d=\frac{10}{-2} \\ d = - 5 \: \: \: \: (B\textsubscript{2}) - 5\\

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