1. Warm up 2. 3.

2. Geometric Sequence
A sequence of terms that have a common ratio between them.

3. Geometric Sequences are Functions
A geometric sequence is a function whose domain is a set of consecutive integers starting with 1 (unless otherwise stated).
The range values are the terms (outputs) of the sequence.

4. Domain and Range of a Sequence
Domain: The whole numbers of the terms in your sequence.
Range: The terms of the sequence.
Example: 1, 3, 9, 27, 81 Domain: { 1, 2, 3,4 ,5 } (5 terms in the sequence) Range: { 1, 3, 9, 27, 81} (same as the sequence itself)

5. Explicit Formula
Formula used to find the nth term of a sequence

6. Explicit Formula for Geometric Sequence
Where a1 is the first term in the sequence and
r is the common ratio

7. Recursive Formula for Geometric Sequence
Where a1 is the first term in the sequence and
r is the common ratio

8. Vocabulary (REVIEW):
Closed/Explicit Formula ‐ A formula for a sequence that is defined by the number of the term and goes directly to that term.
Recursive Formula ‐ A sequence of numbers created by defining a term in the sequence and the pattern created by the sequence using previous terms.

9. Two ways to define sequences

10. Both Formulas need to be in notes!!!

11. Geometric Sequence
Example 1: Find the common ratio
r = 2

12. r = 1/4 Geometric Sequence Example 2 : Find the common ratio
256, 64, 16, 4, …
r = 1/4

13. Example 3: Find the common ratio, the explicit formula, and the seventh term.
6, 3, 1.5, 0.75 …

14. Example 4: Find the common ratio, the explicit formula, and the tenth term.
-4, -12, -36, -108 …

15. Example 5 : The fifth term is 1,792. The common ratio is 4
Example 5 : The fifth term is 1,792. The common ratio is 4. Write the explicit formula.

16. Example 6 : During the month of October, a few teachers decided to spread some holiday fun by starting a game of getting “boo”ed. On the first day, 3 teachers were given “boo” bags and directions to “boo” 2 other teachers. If every teacher followed the directions to “boo” 2 teachers with candy and a sign, find the following:
a. The explicit formula b. The first 4 terms
3, 6, 12, 24…