Question

An electrician earns $110 after his first hour of working for a client. His total pay based on the number of hours worked can be represented using the sequence shown.

110, 130, 150, 170, ...
Which recursive formula can be used to determine the total amount of money earned for each successive hour worked based on the amount of money currently earned?

f(n + 1) = f(n) + 20
f(n + 1) = f(n) + 110
f(n + 1) = f(n + 1) + 20
f(n + 1) = f(n + 1) + 110

What is the common difference between successive terms in the sequence?

9, 2.5, –4, –10.5, –17, ...

–11.5
–6.5
6.5
11.5

Answer 1

1) f(n + 1) = f(n) + 20 (each hour adds $20: 110 → 130 → 150 → 170)

2) Common difference = -6.5 (each term decreases by 6.5: 9 → 2.5 → -4 → -10.5 → -17)