Question

A job pays a salary of $8.50 an hour for the first year and $8.85 an hour for the second year. The hourly salary for year n follows an arithmetic sequence.

Part A: Write a recursive rule for the hourly salary.
Part B: Write an explicit rule for the hourly salary.

Answer 1

The answers to the question above are "a1=8.5; an=an-1+0.35" and "f(n) = 8.5+ 0.35(n - 1)" which is the recursive rule and the explicit rule of the sequence. The Recursive rule could be started with a different number other than the 8.5 but the explicit rule always uses the 8.5 as the starting number.

Answer 2

This is the concept of geometric series. We are required to find the recursive formula for year n. Here we will use the formula;
nth=ar^(n-1)
where;
a=first term
r=common ratio
n=nth term
Thus
a=8.50
r=(8.85)/(8.50)=1.0412
thus the formula will be:
nth=8.50(1.0412)^n