1. Patterns & Sequences
Algebra I, 9/13/17

2. 2 types of recursive formulas
Arithmetic sequence
An arithmetic sequence goes from one term to the next by always adding (or subtracting) the same value.
Do you add, or subtract, the same amount from one term to the next?
2 types of recursive formulas
Geometric sequence
A geometric sequence goes from one term to the next by always multiplying (or dividing) by the same value.
Do you multiply, or divide, the same amount from one term to the next?

3. Arithmetic Sequence “common difference”
How to find an Arithmetic Sequence
Determine if the sequence is arithmetic (Do you add, or subtract, the same amount from one term to the next?)
Find the common difference. (The number you add or subtract.)
Create a recursive formula by stating the first term, and then stating the formula to be the previous term plus the common difference.
Arithmetic Sequence “common difference”

4. a1 = first term; an = a + (n – 1)d
a1 = the first term in the sequence an = the nth term in the sequence  n = the term number d = the common difference.
Example:
Arithmetic Sequence
{10, 15, 20, 25, 30, 35, ...}
first term = 10,
common difference = 5 recursive formula: 
a1= 10; an= an-1 + 5

5. Geometric Sequence “common ratio”
How to find a Geometric Sequence
Determine if the sequence is geometric (Do you multiply, or divide, the same amount from one term to the next?)
Find the common ratio. (The number you multiply or divide.)
Create a recursive formula by stating the first term, and then stating the formula to be the common ratio times the previous term.
Geometric Sequence “common ratio”

6. a1 = first term; an = ar(n – 1)
a1 = the first term in the sequence an = the nth term in the sequence n = the term number r = the common ratio
Example:
Geometric Sequence
{3, 6, 12, 24, 48, 96, ...}
first term = 3, common ratio = 2 explicit formula: 
an= 3 • 2n-1