Geometric sequences

Have a common difference MULTIPLY to get next term Arithmetic Sequences Geometric Sequences ADD To get next term Have a common difference MULTIPLY to get next term Have a common ratio

Try to think of some geometric sequences on your own! In a geometric sequence, the ratio of any term to the previous term is constant. You keep multiplying by the SAME number each time to get the sequence. This same number is called the common ratio and is denoted by r What is the difference between an arithmetic sequence and a geometric sequence? Try to think of some geometric sequences on your own!

Find r for the following sequences 4, 8, 16, 32... r=2 r=3 8, 24, 72, 216... r=4 6, 24, 96, 384... No common ratio! Geometric Sequence 5, 10, 15, 20...

Writing a rule To write a rule for the nth term of a geometric sequence, use the formula:

Writing a rule Write a rule for the nth term of the sequence 6, 24, 96, 384, . . .. Then find This is the general rule. It’s a formula to use to find any term of this sequence. To find , plug 7 in for n.

Writing a rule Write a rule for the nth term of the sequence 1, 6, 36, 216, 1296, . . .. Then find This is the general rule. It’s a formula to use to find any term of this sequence. To find , plug 8 in for n.

Writing a rule Write a rule for the nth term of the sequence 7, 14, 28, 56, 128, . . .. Then find

(when you're not given the first term) Writing a rule (when you're not given the first term) One term of a geometric sequence is The common ratio is r = 3. Write a rule for the nth term.

(when you're given two non-consecutive terms) Writing a rule (when you're given two non-consecutive terms) One term of a geometric sequence is and one term is Step 1: Find r -divide BIG small -find the distance between the two terms and take that root. Step 2: Find . Plug r, n, and into your equation. Then, solve for . Step 3: Write the equation using r and .

(when you're given two non-consecutive terms) Writing a rule (when you're given two non-consecutive terms) Write the rule when and .

Graphing the sequence Let’s graph the sequence we just did. Create a table of values. What kind of function is this? What is a? What is b? Why do we pick all positive whole numbers? Domain, Input, X Range, Output, Y

Think about it.. Work: Pg 145; 1-11 all Does it make sense to connect the dots on our last graph? Why or why not? Work: Pg 145; 1-11 all