Answer
$S_{15}=165$
Work Step by Step
Note that from $a_2$, you have to add the common difference thrice to get the value of $a_5$.
This means that
$a_5=a_2+3d$
With $a_2=8$ and $a_5=9.5$, substituting these values to the equation above gives:
$a_5=a_2+3d
\\9.5=8+3d
\\9.5-8=8+3d-8
\\1.5=3d
\\\dfrac{1.5}{3} = \dfrac{3d}{3}
\\0.5=d$
With $d=0.5$ and $a_2=8$, the first term can be found by subtracting $d$ to $a_2$:
$a = a_2 -d
\\a=8-0.5
\\a=7.5$
RECALL:
The sum of the first $n$ terms of an arithmetic sequence is given by the formula:
$S_n=\dfrac{n}{2}[2a + (n-1)d]$
where
$a$ = first term
$d$ = common difference
Using the formula above, the sum of the first 15 terms of the given arithmetic sequence is:
$S_n = \dfrac{n}{2}[2a + (n-1)d]
\\S_{15}=\dfrac{15}{2}[2(7.5)+(15-1)0.5]
\\S_{15}=\dfrac{15}{2}[15+14(0.5)]
\\S_{15}=\dfrac{15}{2}(15+7)
\\S_{15}=\dfrac{15}{2}(22)
\\S_{15}=165$