Answer
arithmetic,
$d= -\frac{1}{2}$,
$S_n= -\frac{1}{4}n(n-27)$.
Work Step by Step
1. Based on the given sequence, we can determine that it is arithmetic,
2. We can find the common difference as $d=a_2-a_1=-\frac{1}{2}$,
3. We can find the sum of the first n terms as $S_n=\frac{n(2a_1+(n-1)d)}{2}=\frac{n(2(-\frac{1}{2}+7)-\frac{1}{2}(n-1))}{2}=-\frac{1}{4}n(n-27)$.
