Respuesta :

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

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