Section 11 2 geometric sequences
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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 11.2 Geometric Sequences

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Section 11 2 geometric sequences

Section 11.2Geometric Sequences

Objective:

Identify and generate geometric sequences


Vocabulary

Vocabulary

  • Geometric Sequence: multiplying each term by a common ratio (r).

    Remember division is multiplication by a fraction.


Example 3 1a

Multiple-Choice Test Item

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

A 972

B 4

C 0

D –12

Read the Test Item

Sincethe sequence has the common ratio of

Example 3-1a


Example 3 1a1

Solve the Test Item

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

Example 3-1a

Answer: B


Example 3 1b

Multiple-Choice Test Item

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

A 200

B 0

C 12.5

D –12.5

Example 3-1b

Answer: C


Formulas

Formulas

  • Recursive Formula:

  • Explicit Formula:


Example 3 2a

Find the sixth term of a geometric sequence for whichand

Formula for the nth term

Multiply.

Example 3-2a

Answer: The sixth term is 96.


Example 3 2b

Find the fifth term of a geometric sequence for whichand

Example 3-2b

Answer: The fifth term is 96.


Example 3 3a

Formula for the nth term

Answer: An equation is

Example 3-3a

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


Example 3 3b

Answer: An equation is .

Example 3-3b

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


Example 3 4a

Find the seventh term of a geometric sequence for whichand

First find the value of

Formula for the nth term

Divide by 4.

Example 3-4a


Example 3 4a1

Formula for the nth term

Use a calculator.

Example 3-4a

Now find a7.

Answer: The seventh term is 1536.


Example 3 4b

Find the sixth term of a geometric sequence for whichand

Example 3-4b

Answer: The sixth term is 243.


Example 3 5a

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.


Example 3 5a1

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

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

Assignment

  • Page 603

  • # 2- 54 every other even


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