The options that explain the sequence are:
Option A: r(1) = 2; r(n) = r(n - 1) + 3 for n
Option E: r(n) = 3n - 1
How to find the Sequence Pattern?
The general form for an arithmetic sequence is:
aₙ = a + (n - 1)d
where:
a is first term
d is common difference
We are told that she designed 2 rings in the first hour. Thus:
r(1) = 2
Every additional hour, she designs 3 new rings. Thus, the common difference is 3. Thus, we have:
r(n) = 2 + (n - 1)3
r(n) = 2 + 3n - 3
r(n) = 3n - 1
We can also write:
r(n) = r(n - 1) + 3