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# Section 11.2 Geometric Sequences - PowerPoint PPT Presentation

Section 11.2 Geometric Sequences. Objective: Identify and generate geometric sequences . Vocabulary . Geometric Sequence: multiplying each term by a common ratio (r ). Remember division is multiplication by a fraction. Multiple-Choice Test Item.

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### Section 11.2Geometric Sequences

Objective:

Identify and generate geometric sequences

• 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

Since the sequence has the common ratio of

Example 3-1a

To find the missing term, multiply the last given term by

Example 3-1a

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

A 200

B 0

C 12.5

D –12.5

Example 3-1b

• Recursive Formula:

• Explicit Formula:

Formula for the nth term

Multiply.

Example 3-2a

Answer: The sixth term is 96.

Example 3-2b

Answer: The fifth term is 96.

Formula for the nth term

Example 3-3a

Write an equation for the nth term of the geometricsequence5, 10, 20, 40, ….

Example 3-3b

Write an equation for the nth term of the geometricsequence2, 6, 18, 54, ….

First find the value of

Formula for the nth term

Divide by 4.

Example 3-4a

Formula for the nth term

Use a calculator.

Example 3-4a

Now find a7.

Answer: The seventh term is 1536.

Example 3-4b

Answer: 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 3-5a

Find three geometric means between 3.12 and 49.92.

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.

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.

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