Answer
a. $0,\displaystyle \frac{1}{2},1,\frac{3}{2},2$
b. $\displaystyle \frac{1}{2}$
c. see below
.
Work Step by Step
$a_{1}=\displaystyle \frac{1}{2}(1-1)=0$
$a_{2}=\displaystyle \frac{1}{2}(2-1)=\frac{1}{2}$
$a_{3}=\displaystyle \frac{1}{2}(3-1)=1$
$a_{4}=\displaystyle \frac{1}{2}(4-1)=\frac{3}{2}$
$a_{5}=\displaystyle \frac{1}{2}(5-1)=2$
(b)
$\displaystyle \frac{1}{2}-0=\frac{1}{2}$
$1-\displaystyle \frac{1}{2}=\frac{1}{2}$
$\displaystyle \frac{3}{2}-1=\frac{1}{2}$
$2-\displaystyle \frac{3}{2}=\frac{1}{2}$
The common difference is $\displaystyle \frac{1}{2}$.
(c) graphed using desmos.com