Answer:
Common Difference(d) is
[tex]d=\frac{1}{6}[/tex]
Step-by-step explanation:
Given sequence is :
[tex]\frac{1}{6}, \frac{1}{3} ,\frac{1}{2} ,\frac{2}{3} .........[/tex]
If a sequence has a constant common difference throughout the sequence, then the sequence is called Arithmetic Progression.
Considering a sequence:
[tex]a_1,a_2,a_3,a_4..........\\[/tex]
[tex]a_2-a_1=a_3-a_2=a_4-a_3=a_n-a_n_-_1=d[/tex]
where 'd' is the common difference of the A.P.
Similarly, finding the common difference of the given sequence.
[tex]\frac{1}{3} -\frac{1}{6}= \frac{1}{2}- \frac{1}{3}=\frac{2}{3} - \frac{1}{2}=d\\[/tex]
[tex]d=\frac{1}{3}-\frac{1}{6}=\frac{(2)(1)-(1)(1)}{6}=\frac{1}{6}[/tex]
[tex]d=\frac{1}{6}[/tex]
Common Difference(d) is
[tex]d=\frac{1}{6}[/tex]
