Answer
The sequence is arithmetic.
$a_{n}=-3n+51$
Work Step by Step
$a_{2}-a_{1}=45-48=-3$
$a_{3}-a_{2}=42-45=-3$
$a_{4}-a_{3}=39-42=-3$
$a_{5}-a_{4}=36-39=-3$
$a_{6}-a_{5}=33-36=-3$
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.
$a_{1}=48$, $d=-3$
$\implies a_{n}=48+(n-1)(-3)$
or $a_{n}=48-3n+3=-3n+51$
