We are given the following sequence:
[tex]-102,-98,-94,-90[/tex]This is an arithmetic sequence that means that each term can be found by adding a constant term to the previous term. In this case, that constant term is 4, since:
[tex]\begin{gathered} -102+4=-98 \\ -98+4=-94 \\ -94+4=-90 \end{gathered}[/tex]This term is called the common difference. The n-th term of an arithmetic sequence is given by:
[tex]a_n=a_1+(n-1)d[/tex]Where:
[tex]\begin{gathered} a_1=\text{first term} \\ d=\text{common difference} \end{gathered}[/tex]In this case, we have:
[tex]a_n=-102+(n-1)4[/tex]Solving the operations we get:
[tex]a_n=-102+4n-4[/tex]Simplifying:
[tex]a_n=-106+4n[/tex]Now we replace "n = 55" since we want to find the 55th term:
[tex]a_{55}=-106+4(55)[/tex]Solving the operations:
[tex]a_{55}=114[/tex]Therefore the 55th term is 114