Given the sequence below
[tex]2,5,10,17[/tex]It follows the rule
[tex]S_n=n^2+1[/tex]Where
[tex]undefined[/tex][tex]n\text{ is the number of terms}[/tex]Where
[tex]\begin{gathered} n=1 \\ S_n=n^2+1=1^2+1=1+1=2 \end{gathered}[/tex]Where
[tex]\begin{gathered} n=2 \\ S_n=n^2+1=2^2+1=4+1=5 \end{gathered}[/tex]Where
[tex]\begin{gathered} n=3 \\ S_n=n^2+1=3^2+1=9+1=10 \end{gathered}[/tex]Where
[tex]\begin{gathered} n=4 \\ S_n=n^2+1=4^2+1=16+1=17 \end{gathered}[/tex]For the 5th term,
Where
[tex]S_n=n^2+1=5^2+1=25+1=26[/tex]Hence, the sequence is
[tex]S_n=n^2+1[/tex]