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Geometric Sequences & Series

Analyze and understand geometric sequences and series, learn to find the common ratio, nth term, and sum of terms. Explore the relationship between geometric sequences and exponential functions.

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Geometric Sequences & Series

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  1. Geometric Sequences & Series M2S Unit 5a: Day 9 EQ: How do we analyze geometric sequences & series?

  2. Vocabulary In a geometric sequence, the ratio of any term to the previous term is constant. This common ratio is denoted by r. Ex: Watch me as I work one… Tell whether the sequence is geometric. Explain. Geometric; r=2

  3. Tell whether the sequence is geometric. Explain.

  4. Vocabulary Thenth term of a geometric sequence with first term and common ratio r is... Write a rule for the nth term of the geometric sequence.

  5. Write a rule and graph. Create a table of values for the sequence. Notice the points lie on an exponential curve.

  6. Write a rule and graph. Create a table of values for the sequence. Notice the points lie on an exponential curve.

  7. Write a rule and graph. Create a table of values for the sequence. Notice the points lie on an exponential curve.

  8. Relationship between geometric sequences and exponential functions The common ratio (r) will always represent the base (b) in an exponential function. The first term will always be “a” The exponent will always be “n-1” The graph of a geometric sequence will always resemble part of an Exponential function.

  9. 8. Pick the exponential function related to the given geometric sequence. Sequence: 4, 16, 64, 256, 1024, …

  10. 9. Pick the exponential function related to the given geometric sequence. Sequence: 2, 6, 18, 54, …

  11. 10. Pick the exponential function related to the given geometric sequence. Sequence: 90, 30, 10, 10/3, …

  12. Let’s write the rule. Watch me as I work one.Write a rule for the nth term as an exponential function.

  13. Now you try.Give the exponential function that corresponds.

  14. Vocabulary An expression formed by adding the terms of a geometric sequence is called a geometric series. The sum of the first n terms of a geometric series with common ratio r ≠ 1 is:

  15. Find the sum of a geometric series.Watch me as I work one… Find the sum of the first 8 terms (by hand)

  16. Find the sum of a geometric series.Now you try. Find the sum of the first 6 terms. Find the sum of the first 10 terms.

  17. Homework Unit 5a Day 9 Handout

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