Noa makes $48000 in her1 st year working,$56000 in her2 nd year,$64000 in her 3rd year, and so on. Assume the pattern continues. How much will Noa make in her th year working?

Answer 1

Noa's earnings increase by $8,000 each year. We can express her earnings for each year using the following pattern:

• Year 1: $48,000
• Year 2: $56,000
• Year 3: $64,000

We can notice that the earnings form an arithmetic sequence where:

• First term (\(a\)) = $48,000
• Common difference (\(d\)) = $8,000

The formula for the \(n\)-th term of an arithmetic sequence is given by:

\[ a_n = a + (n-1) \cdot d \]

Substituting \(a\) and \(d\):

\[ a_n = 48000 + (n-1) \cdot 8000 \]

Simplifying this:

\[ a_n = 48000 + 8000(n-1) \] \[ a_n = 48000 + 8000n - 8000 \] \[ a_n = 40000 + 8000n \]

So, Noa's earnings in her \(n\)-th year will be:

\[ a_n = 8000n + 40000 \]

Therefore, Noa will make \(8000n + 40000\) in her \(n\)-th year working.