Question

Mr. Red's first year salary is $30,000 and it increases by $500 each year. What is the

explicit rule for this sequence in simplified form?

Answer 1

The answer is
`a_(n) =500n+29,500.`

The recursive rule is
`a_(n) =a_(n-1) + 500`;
`a_(1)=30,000`. In other words, the nth term is the previous term + 500. The first term, as given, is a1 = 30,000.

Explanation:

The answer is
`a_(n) =500n+29,500.`a_n = 500n + 29,500. It is easy to check: just plug in n = 1, and you'll get the first year's salary = 500•1 + 29,500 = 30,000.

Another way to find it is
`a_(n) =30,000+500(n-1)=30,000+500n-500=29,500+500n`.

The recursive rule is
`a_(n) =a_(n-1) + 500`;
`a_(1)=30,000`. In other words, the nth term is the previous term + 500. The first term, as given, is
`a_(1)=30,000`.

Answer 2

`a_(n) =500(n) + 30,000`

Explanation:

Hey there!

This equasion is correct because
`500` is being multiplied by the multiplyer which is
`n`, how many years have gone by

After that The equasion adds
`30,000` because he started with
`30,000`.