Answer:
(a)Common Difference[tex]=-\dfrac{1}{6}[/tex]
(b)Not an arithmetic sequence.
Step-by-step explanation:
An arithmetic sequence is a sequence in which the next term is obtained from the previous term by the addition of a common constant.
(a)Given the sequence:
[tex]\dfrac{1}{2}, \dfrac{1}{3},\dfrac{1}{6},0,\cdots\\\dfrac{1}{3}-\dfrac{1}{2}=-\dfrac{1}{6}\\\dfrac{1}{6}-\dfrac{1}{3}=-\dfrac{1}{6}\\0-\dfrac{1}{6}=-\dfrac{1}{6}[/tex]
Clearly, this is an arithmetic sequence and the common difference is [tex]-\dfrac{1}{6}[/tex]
(b)Given the Sequence:
-3, -7, -10, -14 …
-7-(-3)=-7+3=-4
-10-(-7)=-10+7=-3
-14-(-10)=-14+10=-4
This is not an arithmetic sequence as the constant term is not the same all true.
