Question

avery just got hired for a new job and will make $55,000 in her first year. avery was told that she can expect to get raises of $1,500 every year going forward. how much money in salary would avery make in her 18th year?

Explanation:

Step1: Identify the sequence type

This is an arithmetic sequence problem where the first term \(a_1 = 55000\), the common difference \(d = 1500\), and we need to find the 18th term \(a_{18}\).

Step2: Use the arithmetic sequence formula

The formula for the \(n\)-th term of an arithmetic sequence is \(a_n=a_1+(n - 1)d\). Substitute \(n = 18\), \(a_1=55000\), and \(d = 1500\) into the formula.
\[

$$\begin{align*} a_{18}&=55000+(18 - 1)\times1500\\ &=55000+17\times1500\\ &=55000 + 25500\\ &=80500 \end{align*}$$

\]

Answer:

\(80500\)