10.1 Sequences and Series Fri Nov 1

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# 10.1 Sequences and Series Fri Nov 1 - PowerPoint PPT Presentation

10.1 Sequences and Series Fri 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

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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