Notes – Geometric Sequences



Notes – Geometric Sequences

Arithmetic sequences – _____________ a constant to get the next term (common ____________)

1, 4, 7, 10, 13, …. 15, 11, 7, 3, ….

Geometric sequences - __________ a constant to get the next term

2, 4, 8, 16, 32, ….. 9, -3, 1, -1/3, …..

In a geometric sequence, the __________ of any term to the previous term is ______________.

You keep ______________ by the SAME number to get the next number in the sequence.

The same number is called the _____________ and is denoted by __________.

Find r for the following sequences. Write a ratio [pic] , then simplify.

1. 4, 8, 16, 32

2. 8, 24, 72, 216

3. 6, 2, 2/3, 2/9

4. 5, 10, 15, 20

Writing a rule for a geometric sequence:

[pic]

r is the _________________, a1 is the ________________, n is the _________________

Example 1: Write a rule for the nth term of the sequence 6, 24, 96, 384, … Then find a7.

Example 2: Write a rule for the nth term of the sequence 1, 6, 36, 216, 1296, Then find a8.

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

7, 14, 28, 56, 128, . . .

Then find

Writing a rule when you’re not given the first term

1. Use the formula to find the first term. Plug in values for r, n, and an…and solve for a1.

2. Write the rule for the nth term. Use the basic formula and plug in r, and a1.

Example 3: If a3 = 18 and the common ratio is 3, write a rule for the nth term.

Now You Try: If a4=8 and the common ratio is 2, write a rule for the nth term.

Graphing the sequence

1. The domain is all positive integers (1,2, 3, 4, 5, …)

2. Plug in these values to find the y values

3. Plot the points and connect with a smooth curve.

Example 4: Graph the sequence from the Example 3: [pic]

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any term

the previous term

[pic]

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