Answer
a. $\displaystyle \frac{5}{2},-\frac{3}{2},-\frac{11}{2},-\frac{19}{2},-\frac{27}{2}$
b. $-4$
c. see below
.
Work Step by Step
a.
$a_{1}=\displaystyle \frac{5}{2}-(1-1)=\frac{5}{2}$
$a_{2}=\displaystyle \frac{5}{2}-(2-1)=-\frac{3}{2}$
$a_{3}=\displaystyle \frac{5}{2}-(3-1)=-\frac{11}{2}$
$a_{4}=\displaystyle \frac{5}{2}-(4-1)=-\frac{19}{2}$
$a_{5}=\displaystyle \frac{5}{2}-(5-1)=-\frac{27}{2}$
(b)
$-\displaystyle \frac{3}{2}-(\frac{5}{2})=-\frac{8}{2}=-4$
$-\displaystyle \frac{11}{2}-(-\frac{3}{2})=-\frac{8}{2}=-4$
$-\displaystyle \frac{19}{2}-(-\frac{11}{2})=-\frac{8}{2}=-4$
$-\displaystyle \frac{27}{2}-(-\frac{19}{2})=-\frac{8}{2}=-4$
The common difference is $-4$.
(c) graphed using desmos.com
