Answer
The sequence is arithmetic.
Common difference $d=-\frac{1}{2}$
Work Step by Step
We compute the difference between each term and the preceding term. If the difference is same, then the sequence is arithmetic.
$a_{2}-a_{1}=\frac{7}{2}-4=-\frac{1}{2}$
$a_{3}-a_{2}=3-\frac{7}{2}=-\frac{1}{2}$
$a_{4}-a_{3}=\frac{5}{2}-3=-\frac{1}{2}$
$a_{5}-a_{4}=2-\frac{5}{2}=-\frac{1}{2}$
$a_{6}-a_{5}=\frac{3}{2}-2=-\frac{1}{2}$
$a_{7}-a_{6}=1-\frac{3}{2}=-\frac{1}{2}$
The difference between each term and preceding term is constant and therefore the sequence is arithmetic.
Common difference $d=-\frac{1}{2}$
