Answer
The sequence is arithmetic.
Common difference $d=-\frac{5}{2}$
$a_{n}=-\frac{5}{2}n+\frac{17}{2}$
Work Step by Step
$a_{2}-a_{1}=\frac{7}{2}-6=-\frac{5}{2}$
$a_{3}-a_{2}=1-\frac{7}{2}=-\frac{5}{2}$
$a_{4}-a_{3}=-\frac{3}{2}-1=-\frac{5}{2}$
$a_{5}-a_{4}=-4-(-\frac{3}{2})=-\frac{5}{2}$
$a_{6}-a_{5}=-\frac{13}{2}-(-4)=-\frac{5}{2}$
As the difference between each term and the preceding term is the same, the sequence is arithmetic.
The general term is
$a_{n}=a_{1}+(n-1)d$
where $d$ is the common difference.
$a_{1}=6$, $d=-\frac{5}{2}$
$\implies a_{n}=6+(n-1)(-\frac{5}{2})$
Or $a_{n}=6-\frac{5}{2}n+\frac{5}{2}=-\frac{5}{2}n+\frac{17}{2}$
