What is the common difference in the following arithmetic sequence?
2/3, 1/6, -1/3,-5/6....

Answer:

Common difference[tex]=\frac{-1}{2}[/tex]

Step-by-step explanation:

We have general form of arithmetic sequence

            a, a+d, a+2d, a+3d ...................

Here it is given that the sequence is

            2/3, 1/6, -1/3,-5/6....

Comparing we will get

            [tex]a=\frac{2}{3}[/tex]

            [tex]a+d=\frac{1}{6}\\\\\frac{2}{3}+d=\frac{1}{6}\\\\d=\frac{1}{6}-\frac{2}{3}=\frac{-3}{6}=\frac{-1}{2}[/tex]

So common difference[tex]=\frac{-1}{2}[/tex]