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Section 11.2 Geometric SequencesPowerPoint Presentation

Section 11.2 Geometric Sequences

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Vocabulary

- Geometric Sequence: multiplying each term by a common ratio (r).
Remember division is multiplication by a fraction.

Find the missing term in the geometric sequence 324, 108, 36, 12, ___.

A 972

B 4

C 0

D –12

Read the Test Item

Since the sequence has the common ratio of

Example 3-1aTo find the missing term, multiply the last given term by

Example 3-1aAnswer: B

Find the missing term in the geometric sequence 100, 50, 25, ___.

A 200

B 0

C 12.5

D –12.5

Example 3-1bAnswer: C

Formulas

- Recursive Formula:
- Explicit Formula:

Find the sixth term of a geometric sequence for which and

Formula for the nth term

Multiply.

Example 3-2aAnswer: The sixth term is 96.

Find the fifth term of a geometric sequence for which and

Example 3-2bAnswer: The fifth term is 96.

Formula for the nth term

Answer: An equation is

Example 3-3aWrite an equation for the nth term of the geometricsequence5, 10, 20, 40, ….

Answer: An equation is .

Example 3-3bWrite an equation for the nth term of the geometricsequence2, 6, 18, 54, ….

Find the seventh term of a geometric sequence for which and

First find the value of

Formula for the nth term

Divide by 4.

Example 3-4aFormula for the nth term

Use a calculator.

Example 3-4aNow find a7.

Answer: The seventh term is 1536.

Find the sixth term of a geometric sequence for which and

Example 3-4bAnswer: The sixth term is 243.

Use the nth term formula to find the value of r. In the sequence 3.12, ___, ___, ___, 49.92, a1 is 3.12 and a5is 49.92.

Formula for the nth term

Divide by 3.12.

Take the fourth root of each side.

Example 3-5aFind three geometric means between 3.12 and 49.92.

Example 3-5a

There are two possible common ratios, so there are twopossible sets of geometric means. Use each value of rto find three geometricmeans.

Answer: The geometric means are 6.24, 12.48, and 24.96, or –6.24, 12.48, and –24.96.

Example 3-5b

Find three geometric means between 12 and 0.75.

Answer: The geometric means are 6, 3, and 1.5, or –6, 3, and –1.5.

Assignment

- Page 603
- # 2- 54 every other even

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