We are given the following sequence:
[tex]7,10,13[/tex]We notice that each term is determined by adding 3 to the previous, therefore, this is an arithmetic sequence and the common difference is 3. The nth term of an arithmetic sequence is:
[tex]a_n=a_1+(n-1)d[/tex]Where a1 is the first term and "d" is the common difference. Replacing the values we get:
[tex]a_n=7+(n-1)(3)[/tex]Simplifying:
[tex]\begin{gathered} a_n=7+3n-3 \\ a_n=4+3n \end{gathered}[/tex]Now we replace n = 33 in the formula:
[tex]\begin{gathered} a_{33}=4+3(33) \\ a_{33}=4+99 \\ a_{33}=103 \end{gathered}[/tex]Therefore, the 33rd term is 103.
