We have the following arithmetic sequence:
[tex]2,5,8,11,\ldots[/tex]Now, the general n-term of this sequence can be written in the following way:
[tex]a_n=2+(n-1)\cdot3[/tex]where n takes the following values:
[tex]n=1,2,3,\ldots[/tex]We see that this general term reproduces the sequence about:
[tex]\begin{gathered} a_1=2+(1-1)\cdot3=2+0=2 \\ a_2=2+(2-1)\cdot3=2+3=5 \\ a_3=2+(3-1)\cdot3=2+6=8 \\ a_4=2+(4-1)\cdot3=2+9=11 \\ \ldots \end{gathered}[/tex]We can find the 13th term of sequence simply replacing n by 13 in the general formula above, we get:
[tex]\begin{gathered} n=13\rightarrow a_n=2+(n-1)\cdot3 \\ \rightarrow a_{13}=2+(13-1)\cdot3=2+36=38 \end{gathered}[/tex]Answer
The 13th term of the sequence is:
[tex]a_{13}=38[/tex]