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10.1 Sequences and Series Fri Nov 1PowerPoint Presentation

10.1 Sequences and Series Fri Nov 1

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### 10.1 Sequences and SeriesFri Nov 1

Do Now

State the pattern

1) 0, 1, 3, 6, 10, 15, …

2) 1, 1, 2, 3, 5, 8, 13, 21, …

CH ¾ Test review

- Retakes by next Wed

Sequences

- A finite sequence is a function, where the domain is a set of consecutive positive integers beginning with 1
- An infinite sequence is a function having for its domain the set of all positive integers

Ex

- Find the first 4 terms and the 23rd term of the sequence whose general term I given by

Calculators

- You can use your graphing calculator to see the terms of a sequence
- 1) Type the expression in Y=
- 2) 2nd -> table

Graphs of Sequences

- The graph of a sequence mimics the graph of the identical function, except only the x integers are plotted
- Ex: f(x) = x + 1 and a = n + 1

Finding the general term

- To find the general term, we need to find the pattern and make a prediction.
- Remember: you will always plug in n = 1 first
- Ex:
- 1)
- 2) -1, 3, -9, 27, -81, …
- 3) 2, 4, 8, 16, …

Recursive Sequences

- A sequence may be defined recursively, which uses the previous term to find the new term
- Ex: Find the first 5 terms of the sequence defined by

Closure

- Find the first 4 terms, and the 10th term of the sequence
- HW: p.850 #1-27 odds 61 65 71

10.1 Sums and SeriesMon Nov 4

- Do Now
- Find the first 4 terms of the sequence, then add them together

Series

- A series is the sum of a sequence.
- An infinite series is the sum of the terms of an infinite sequence
- A finite series, or partial sum, is the sum of the first n terms of a sequence
- A finite series, or nth partial sum, is denoted

Ex

- For the sequence -2, 4, -6, 8, -10, 12, -14,…, find each of the following
- 1)
- 2)
- 3)

Sigma Notation

- The Greek letter sigma is used to represent a partial sum or series. This is called sigma notation

Ex

- Find and evaluate each of the following sums
- 1)
- 2)

Ex

- Write sigma notation for each sum
- 1) 1 + 2 + 4 + 8 + 16 + 32 + 64
- 2) -2 + 4 – 6 + 8 – 10
- 3)

Closure

- Find and evaluate the sum
HW: p. 850 #29-59 odds

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