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Geometric Series

Geometric Series. Choi 2012. Recall: What is a Series?. A series is the sum of terms of a sequence. The sum of the first n terms in a sequence is denoted as S n. S 5  t he sum of the first 5 terms. Geometric Series.

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Geometric Series

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  1. Geometric Series Choi 2012

  2. Recall: What is a Series? • A series is the sum of terms of a sequence. • The sum of the first nterms in a sequence is denoted as Sn. S5  the sum of the first 5terms

  3. Geometric Series Recall: A sequence like 2, 6, 18, 54,…, is called aGeometric sequence with a = 2 and r = 3. Therefore a series that corresponds to this geometric sequence is 2 + 6 + 18 + 54 +…, is called ageometric series.

  4. Geometric Series Formula The Sum of the First nterms of a Geometric Series Recall: Geometric Sequence formula Multiply this series by r Subtract this two rows All the terms except the first and last are cancelled out or Formula 2 (Optional) Formula 1

  5. Example 1 – Sum of a Series given the first term Find the sum of the first 9 terms of the geometric series.

  6. Example 2 – Sum of a Series given the first term Find the sum of the first 14 terms of the geometric series.

  7. Example 3 – Sum of a series given first and last terms Find the sum of the geometric series 5 + 20 + 80 + ... + 20480. 7 7 There are 7 terms in the series.

  8. Homework: • P. 476 #1-3 (Every other), 6-8

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