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6.3 Geometric Series

6.3 Geometric Series. 3/25/2013. Geometric Sequence:. Is a sequence where each term is multiplied by the same factor in order to obtain the following term . Example:. 2, 8, 32, 128, 512, . . . . x 4 . x 4 . x 4 . x 4 . Common ratio (r):. 4 . Definition of Geometric Sequence.

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6.3 Geometric Series

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  1. 6.3 Geometric Series 3/25/2013

  2. Geometric Sequence: Is a sequence where each term is multiplied by the same factor in order to obtain the following term. Example: 2, 8, 32, 128, 512, . . . x 4 x 4 x 4 x 4 Common ratio (r): 4

  3. Definition of Geometric Sequence Rule of nth term of a geometric sequence 2, 8, 32, 128, 512, . . . Common ratio, r = 4 1st term: 2nd term: 3rd term: 4th term: What’s the pattern? Rule:

  4. Geometric Series: Expression formed by adding the terms of a geometric sequence. Example (Finite): r Geometric Infinite Series: r

  5. Determine whether the following series is geometric. Explain why or why not. If it is geometric, find the common ratio. Yes Each term is multiplied by 5. r = 5 • Yes • Each term is multiplied by . • r = . No Each term is multiplied by different values. No Each term is multiplied by different values.

  6. Sum of the Finite Geometric Series S = Sum of the series = first term in the series. r = common ratio n = number of terms.

  7. Find the sum of the finite geometric series ++ r = 4 n = since n started at 0 there are 9 terms = 524,286

  8. Find the sum of the finite geometric series r = n = 15 = 13.999957

  9. Sum of the Infinite Geometric Series Only when common ratio is between 0 and 1. S = Sum of the series = first term in the series. r = common ratio

  10. Find the sum of the infinite geometric series r = = 14

  11. Find the sum of the infinite geometric series r = =

  12. Homework WS 6.3 odd problems only “I stayed up all night to see where the sun went. Then it dawned on me.”

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