1. EOC Review:
Explicit & Recursive

2. Exponential functions match geometric sequences
y = a(b)x
initial value rate of change
(y-intercept)
NEXT = b(NOW)
Starting value for recursive form is the first term – not y-intercept.

3. Try creating a table to visualize the patterns.
NEXT = 2(NOW) starting at -4
y = _____ (2)x
Find the y-intercept by reversing the table.

4. Example: E#4.1 A geometric sequence is shown: 32, 16, 8, ...
How do we know it is exponential?
A geometric sequence is shown: 32, 16, 8, ...
Which is the explicit formula for this sequence?
What is the recursive formula?
What is the 6th term?

5. Example E#4.2 How do we know this is exponential?
The recursive formula NEXT = 4 • NOW models the number of people with a virus in a school each week. If there are 36 people infected with the virus after 3 weeks, how many people will be infected after 6 weeks? What is the explicit formula?

6. You Try!
Try making a table to check your patterns & formulas.

7. Check it E#4.3
The explicit formula A = 2(3)n models the growth of a colony of bunnies in a year. What is the recursive formula for this?

8. Check it: E#4.4 A sequence is shown: 2, 6, 18, 54, . . .
Which recursive formula models the sequence?
What is the explicit formula for the sequence?
What is the 10th term?

9. Check it: E#4.5
The recursive formula for a sequence is shown below. NEXT = 2 • NOW, starting at 4 Which explicit formula can be used to determine the value of the nth term in the sequence? What is the 6th term in the sequence?

10. Check it E#4.6
The explicit formula for a geometric sequence is A = 5(1/2)x .
What is the recursive formula?
What is the 5th term in the sequence?