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Section 11.2 Geometric Sequences

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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  1. Section 11.2Geometric Sequences Objective: Identify and generate geometric sequences

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

  3. 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 Since the sequence has the common ratio of Example 3-1a

  4. Solve the Test Item To find the missing term, multiply the last given term by Example 3-1a Answer: B

  5. 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

  6. Formulas • Recursive Formula: • Explicit Formula:

  7. Find the sixth term of a geometric sequence for which and Formula for the nth term Multiply. Example 3-2a Answer: The sixth term is 96.

  8. Find the fifth term of a geometric sequence for which and Example 3-2b Answer: The fifth term is 96.

  9. 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, ….

  10. Answer: An equation is . Example 3-3b Write an equation for the nth term of the geometricsequence2, 6, 18, 54, ….

  11. 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 3-4a

  12. Formula for the nth term Use a calculator. Example 3-4a Now find a7. Answer: The seventh term is 1536.

  13. Find the sixth term of a geometric sequence for which and Example 3-4b Answer: The sixth term is 243.

  14. 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.

  15. 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.

  16. 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.

  17. Assignment • Page 603 • # 2- 54 every other even

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