It's an arithmetic series.
The sum of the first n terms of an arithmetic series:
[tex]S_n=\frac{n(a_1+a_n)}{2}[/tex]
[tex]7, 12, 17,... \\ \\
a_1=7 \\
d=a_2-a_1=12-7=5 \\ a_5=a_3+2d=17+2 \times 5=17+10=27 \\ \\
S_5=\frac{5(7+27)}{2}=\frac{5 \times 34}{2}=5 \times 17=85[/tex]
The sum of the first five terms is 85.
