Answer
The general term $a_n$ is given by the formula:
$a_n=\$4000 + \$125(n-1)$
At the end of his 12-month training, his monthly salary would be $\$5,375$.
Work Step by Step
RECALL:
An arithmetic sequence is a sequence that has a common difference.
The next term of an arithmetic sequence can be found by adding the common difference to the previous term.
Since the his starting salary is $\$4,000$ and he is guaranteed a monthly increase of $\$125$, then the given sequence involves a common difference of $\$125$.
Thus, this sequence is arithmetic.
The given arithmetic sequence has $a_1 = \$4,000$ and a common difference $d=\$125$.
The $n^{th}$ term ($a_n$) of an arithmetic sequence is given by the formula $a_n=a_1 +d(n-1)$ where $a_1$ is the first term and $d$ is the common difference.
Thus, the general term $a_n$ is given by the formula:
$a_n = a_1 +d(n-1)
\\a_n=\$4000 + \$125(n-1)$
Thus, at the end of his 12-month training, his monthly salary would be:
$a_{12} = a_1 + d(12-1)
\\a_{12}=\$4000 + \$125(12-1)
\\a_{12}=\$4000+\$125(11)
\\a_{12}=\$4000+\$1375
\\a_{12}=\$5,375$
