Sequences   finding a rule
Upcoming SlideShare
Loading in...5
×
 

Sequences finding a rule

on

  • 1,229 views

 

Statistics

Views

Total Views
1,229
Slideshare-icon Views on SlideShare
1,229
Embed Views
0

Actions

Likes
0
Downloads
4
Comments
0

0 Embeds 0

No embeds

Accessibility

Categories

Upload Details

Uploaded via as Microsoft PowerPoint

Usage Rights

© All Rights Reserved

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

    Sequences   finding a rule Sequences finding a rule Presentation Transcript

    •  
    • SEQUENCES
      • A sequence is a set of terms, in a definite order, where the terms are obtained by some rule.
      A finite sequence ends after a certain number of terms. An infinite sequence is one that continues indefinitely.
      • For example:
      1, 3, 5, 7, … (This is a sequence of odd numbers) 1st term = 2 x 1 – 1 = 1 2nd term = 2 x 2 – 1 = 3 3rd term = 2 x 3 – 1 = 5 nth term = 2 x n – 1 = 2 n - 1 . . . . . . + 2 + 2
    • NOTATION
      • 1st term = u
      2nd term = u 3rd term = u n th term = u . . . . . . 1 2 3 n
    • OR
      • 1st term = u
      2nd term = u 3rd term = u n th term = u . . . . . . 0 1 2 n-1
    • FINDING THE FORMULA FOR THE TERMS OF A SEQUENCE
      • A recurrence relation defines the first term(s) in the sequence and the relation between successive terms.
      • u = 5
      u = u +3 = 8 u = u +3 = 11 u = u +3 = 3 n + 2 . . . 1 2 3 n+1 For example: 5, 8, 11, 14, … 1 2 n
      • What to look for
      • when looking for the rule
      • defining a sequence
      • Constant difference: coefficient of n is the difference
      • 2 nd level difference: compare with square numbers
      • ( n = 1, 4, 9, 16, …)
      • 3 rd level difference: compare with cube numbers
      • ( n = 1, 8, 27, 64, …)
      • None of these helpful: look for powers of numbers
      • (2 = 1, 2, 4, 8, …)
      • Signs alternate: use (-1) and (-1)
      • -1 when k is odd +1 when k is even
      k k 2 3 n - 1
      • EXAMPLE:
      • Find the next three terms in the sequence 5, 8, 11, 14, …
      • EXAMPLE:
      • The nth term of a sequence is given by x =
      • Find the first four terms of the sequence.
      • b) Which term in the sequence is ?
      • c) Express the sequence as a recurrence relation.
      1 __ 2 n n 1 1024 ____
      • EXAMPLE:
      • Find the nth term of the sequence +1, -4, +9, -16, +25, …
      • EXAMPLE:
      • A sequence is defined by a recurrence relation of the form:
      • M = aM + b .
      • Given that M = 10, M = 20, M = 24, find the value of a and the
      • value of b and hence find M .
      n + 1 1 3 2 4