10 1 sequences and series fri nov 1 n.
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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 series fri nov 1

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 test review
CH ¾ Test review
  • Retakes by next Wed
sequences
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
slide4
Ex
  • Find the first 4 terms and the 23rd term of the sequence whose general term I given by
calculators
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
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
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
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
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 series mon nov 4
10.1 Sums and SeriesMon Nov 4
  • Do Now
  • Find the first 4 terms of the sequence, then add them together
series
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
slide13
Ex
  • For the sequence -2, 4, -6, 8, -10, 12, -14,…, find each of the following
  • 1)
  • 2)
  • 3)
sigma notation
Sigma Notation
  • The Greek letter sigma is used to represent a partial sum or series. This is called sigma notation
slide15
Ex
  • Find and evaluate each of the following sums
  • 1)
  • 2)
slide16
Ex
  • Write sigma notation for each sum
  • 1) 1 + 2 + 4 + 8 + 16 + 32 + 64
  • 2) -2 + 4 – 6 + 8 – 10
  • 3)
closure1
Closure
  • Find and evaluate the sum

HW: p. 850 #29-59 odds