The rules that define the sequence are f(n) = 9n - 14 and f(1) = -5; f(n) = f(n - 1) + 9
How to determine the rules that define the sequence
From the question, we have the following parameters that can be used in our computation:
-5, 4, 13, 22, 31, ...
In the above sequence, we can see that 9 is added to the previous term to get the new term
This means that
First term, a = -5
Common difference, d = 9
The nth term is then represented as
f(n) = a + (n - 1) * d
Substitute the known values in the above equation, so, we have the following representation
f(n) = -5 + 9(n - 1)
f(n) = 9n - 14
The recursive sequence of the above is
f(1) = -5; f(n) = f(n - 1) + 9