Question

find the 55th term in the following arithmetic sequence: -102, -98,-94, -90, ...

Answer 1

We are given the following sequence:

$-102,-98,-94,-90$

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:

$\begin{gathered} -102+4=-98 \\ -98+4=-94 \\ -94+4=-90 \end{gathered}$

This term is called the common difference. The n-th term of an arithmetic sequence is given by:

$a_n=a_1+(n-1)d$

Where:

$\begin{gathered} a_1=\text{first term} \\ d=\text{common difference} \end{gathered}$

In this case, we have:

$a_n=-102+(n-1)4$

Solving the operations we get:

$a_n=-102+4n-4$

Simplifying:

$a_n=-106+4n$

Now we replace "n = 55" since we want to find the 55th term:

$a_{55}=-106+4(55)$

Solving the operations:

$a_{55}=114$

Therefore the 55th term is 114