To find S5 first you need to find a5 (fith term)
Use the given data in the arithmetic sequence formula to find the common difference:
[tex]\begin{gathered} a_n=a_1+(n-1)d \\ \\ a_1=9 \\ a_3=17 \\ n=3 \\ \\ 17=9+(3-1)d \\ 17=9+2d \\ 17-9=2d \\ 8=2d \\ \frac{8}{2}=d \\ \\ d=4 \end{gathered}[/tex]Use the common difference (a1) and the first term (a1) to write the formula of the given sequence:
[tex]a_n=9+(n-1)4[/tex]Find the 5th term:
[tex]\begin{gathered} a_5=9+(5-1)4 \\ a_5=9+4\cdot4 \\ a_5=9+16 \\ a_5=25 \end{gathered}[/tex]Use the formula of Sn (written in the first line in the page) to dinf S5:
[tex]\begin{gathered} S_5=5(\frac{9+25}{2}) \\ \\ S_5=4(\frac{34}{2}) \\ \\ S_5=\frac{136}{2} \\ \\ S_5=68 \end{gathered}[/tex]Then, S5 is 68
[tex]S_5=68[/tex]