Arithmetic Sequences Geometric Sequences ADD To get next

In a geometric sequence, the ratio of any term to the previous term is

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

Example 1: Write a rule for the nth term of the sequence 6, 24,

Example 2: Write a rule for the nth term of the sequence 1, 6,

Now You Try: Write a rule for the nth term of the sequence 7,

Example 3: One term of a geometric sequence is. The common ratio is r

Let’s graph the sequence from Example 3. Create a table of values. Why do

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

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

No common ratio! Geometric Sequence

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

Example 1: 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.

Example 2: 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.

Now You Try: Write a rule for the nth term of the sequence 7, 14, 28, 56, 128, . . . Then find

Example 3: One term of a geometric sequence is. The common ratio is r = 3. Write a rule for the nth term. n is the number of the known term an is the value of the known term

Let’s graph the sequence from Example 3. Create a table of values. Why do we pick all positive whole numbers? Domain, Input, x Range, Output, y What kind of function is this? What is a? What is b?