Pre-Cal 40S Slides January 16,  2008
Upcoming SlideShare
Loading in...5
×
 

Pre-Cal 40S Slides January 16, 2008

on

  • 1,095 views

Arithmetic and geometric sequences; implicit and recursive definitions.

Arithmetic and geometric sequences; implicit and recursive definitions.

Statistics

Views

Total Views
1,095
Slideshare-icon Views on SlideShare
993
Embed Views
102

Actions

Likes
0
Downloads
16
Comments
0

13 Embeds 102

http://pc40sf07.blogspot.com 56
http://2011ecipre-calc30s.blogspot.com 30
http://pc40sf07.blogspot.ca 3
http://www.blogger.com 2
http://pc40sf07.blogspot.com.au 2
http://pc40sf07.blogspot.co.uk 2
http://pc40sf07.blogspot.pt 1
http://pc40sf07.blogspot.nl 1
http://2011ecipre-calc30s.blogspot.ca 1
http://pc40sf07.blogspot.com.es 1
http://www.pc40sf07.blogspot.com 1
http://www.slideshare.net 1
http://pc40sf07.blogspot.mx 1
More...

Accessibility

Categories

Upload Details

Uploaded via as Adobe PDF

Usage Rights

CC Attribution-NonCommercial-ShareAlike LicenseCC Attribution-NonCommercial-ShareAlike LicenseCC Attribution-NonCommercial-ShareAlike License

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
  • Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
    Processing…
Post Comment
Edit your comment

    Pre-Cal 40S Slides January 16,  2008 Pre-Cal 40S Slides January 16, 2008 Presentation Transcript

    • Sequences Photo source chromaspiral
    • Find the next three terms in each sequence of numbers ... 4, 7, 10, 13, , , 3, 6, 12, 24, , , 32, 16, 8, 4, , , 1, 1, 2, 3, 5, 8,13, , ,
    • 4, 7, 10, 13, , , 3n+1
    • 4, 7, 10, 13, , ,
    • 3, 6, 12, 24, , ,
    • Some Definitions Sequence: An ordered list of numbers that follow a certain pattern (or rule). Arithmetic Sequence:(i) Recursive Definition: An ordered list of numbers generated by continuously adding a value (the common difference) to a given first term. (ii) Implicit Definition: An ordered list of numbers where each number in the list is generated by a linear equation. Common Difference (d):(i) The number that is repeatedly added to successive terms in an arithmetic sequence. (ii) From the implicit definition, d is the slope of the linear equation.
    • To Find The Common Difference d is the common difference d = tn - t(n - 1) tn is an arbitrary term in the sequence t(n - 1) is the term immediately before tn in the sequence To Find the nth Term In an Arithmetic Sequence tn is the nth term tn = a + (n - 1)d a is the first term n is the quot;rankquot; of the nth term in the sequence d is the common difference Example: Find the 51st term (t51) of the sequence 11, 5, -1, -7, ... Solution: a = 11 t51 = 11 + (51 - 1)(-6) d = 5 - 11 t51 = 11 + (50)(-6) = -6 t51 = 11 - 300 n = 51 t51 = -289
    • Geometric Sequence: (i) Recursive Definition: An ordered list of numbers generated by continuously multiplying a value (the common ratio) with a given first term. (ii) Implicit Definition: An ordered list of numbers where each number in the list is generated by an exponential equation. Common Ratio (r): (i) The number that is repeatedly multiplied to successive terms in a geometic sequence. (ii) From the implicit definition, r is the base of the exponential function.
    • 3, 6, 12, 24, , ,
    • To Find The Common Ratio r is the common ratio tn is an arbitrary term in the sequence t(n - 1) is the term immediately before tn in the sequence To Find the nth Term In a Geometic Sequence tn is the nth term a is the first term n is the quot;rankquot; of the nth term in the sequence r is the common ratio