Answer
See below.
Work Step by Step
In order for a sequence to be arithmetic, the difference of all consecutive terms must be constant.
Hence here: $d=-0.5$, which is constant thus it is an arithmetic sequence.
The sum of the first $n$ terms of an arithmetic sequence can be obtained by the following formula: $\frac{n(a_1+a_n)}{2},$ where $a_1$ is the first term, $a_n$ is the nth term and $n$ is the number of terms.
The nth term of an arithmetic sequence can be obtained by the following formula: $a_n=a_1+(n-1)d$, where $a_1$ is the first term and $d$ is the common difference.
Hence here: $a_1=-0.5+7=6.5,a_{n}=6.5+(n-1)(-0.5)=6.5-0.5n+0.5=7-0.5n$
Thus the sum:$\frac{n(6.5+(7-0.5n))}{2}=\frac{n(13.5-0.5n)}{2}$
