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Geometric Sequences

Geometric Sequences. 2, 6, 18, 54, 162, … 200, 20, 2, .2, … In a geometric sequence, each term is obtained by multiplying the previous one by a fixed quantity (called the common ratio ). Formula for a Geometric Sequence. u n = a(r) n - 1. Example 1.

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Geometric Sequences

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  1. Geometric Sequences

  2. 2, 6, 18, 54, 162, … • 200, 20, 2, .2, … In a geometric sequence, each term is obtained by multiplying the previous one by a fixed quantity (called the common ratio)

  3. Formula for a Geometric Sequence un = a(r)n -1

  4. Example 1 • Find the 10th term of the sequence 2, 6, 18, 54, 162, …

  5. You Do 1 • Find the 15th term of the sequence 200, 20, 2, .2, …

  6. Example 2 • Find the 11th term of the sequence 1, -1/2, ¼, -1/8, 1/16, …

  7. Example 3 • A geometric sequence has a fifth term of 3 and a seventh term of 0.75. Find the first term, the common ratio, and the tenth term.

  8. Example 4 • Find the number of terms in the geometric sequence .25, .75, 2.25, …, 44286.75

  9. You Do 2 • The third and seventh terms of a geometric sequence are ¾ and 12 respectively. (a) Find the 10th term. (b) What term is equal to 3072?

  10. Example 5 • A car originally worth $34,000 loses 15% of its value each year. (a) Write a geometric sequence that gives the year by year value of the car. (b) Find the value of the car after 6 years. (c) After how many years will the value of the car fall below $10,000?

  11. Example 5… • A car originally worth $34,000 loses 15% of its value each year. (a) Write a geometric sequence that gives the year by year value of the car.

  12. Example 5… • A car originally worth $34,000 loses 15% of its value each year. (b) Find the value of the car after 6 years.

  13. Example 5… • A car originally worth $34,000 loses 15% of its value each year. (c) After how many years will the value of the car fall below $10,000?

  14. You Do 3 • The number of people in a small country town increases by 2% each year. If the population at the start of 1970 was 12500, what is the predicted population at the start of the year 2010?

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