Answer
It is an arithmetic sequence.
$d=\frac{1}{4}$
Work Step by Step
A sequence is arithmetic if $a_2−a_1=a_3−a_2=a_4−a_3=a_5−a_4=...=d$
For the given sequence we have that:
$a_2-a_1=\frac{3}{2}-\frac{5}{4}=\frac{3(2)}{2(2)}-\frac{5}{4}=\frac{6}{4}-\frac{5}{4}=\frac{1}{4}$
$a_3-a_2=\frac{7}{4}-\frac{3}{2}=\frac{7}{4}-\frac{3(2)}{2(2)}=\frac{7}{4}-\frac{6}{4}=\frac{1}{4}$
$a_4-a_3=2-\frac{7}{4}=\frac{2(4)}{4}-\frac{7}{4}=\frac{8}{4}-\frac{7}{4}=\frac{1}{4}$
$a_5-a_4=\frac{9}{4}-2=\frac{9}{4}-\frac{2(4)}{4}=\frac{9}{4}-\frac{8}{4}=\frac{1}{4}$
It is an arithmetic sequence.
Common difference: $d=\frac{1}{4}$
