slide1 l.
Download
Skip this Video
Download Presentation
SEQUENCES

Loading in 2 Seconds...

play fullscreen
1 / 15

SEQUENCES - PowerPoint PPT Presentation


  • 171 Views
  • Uploaded on

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. 1, 3, 5, 7, … (This is a sequence of odd numbers).

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'SEQUENCES' - keziah


Download Now An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
slide2
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.

slide3

1, 3, 5, 7, …

(This is a sequence of odd numbers)

1st term = 2 x 1 – 1 = 1

For example:

+ 2

2nd term = 2 x 2 – 1 = 3

+ 2

3rd term = 2 x 3 – 1 = 5

. .

. .

. .

nth term = 2 x n – 1 = 2n - 1

notation
NOTATION

1

2nd term = u

1st term = u

2

3rd term = u

3

. .

. .

. .

nth term = u

n

slide5
OR

0

2nd term = u

1st term = u

1

3rd term = u

2

. .

. .

. .

nth term = u

n-1

slide7
A recurrence relation defines the first term(s) in the sequence and the relation between successive terms.
slide8

For example:

5, 8, 11, 14, …

1

u = u +3 = 8

u = 5

1

2

u = u +3 = 11

3

2

.

.

.

u = u +3 = 3n + 2

n+1

n

slide9
What to look for

when looking for the rule

defining a sequence

slide10

2

  • Constant difference: coefficient of n is the difference
  • 2nd level difference: compare with square numbers

(n = 1, 4, 9, 16, …)

  • 3rd 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

3

n - 1

k

k

slide11
EXAMPLE:

Find the next three terms in the sequence 5, 8, 11, 14, …

slide12

1

__

n

n

2

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

____

1024

slide13
EXAMPLE:

Find the nth term of the sequence +1, -4, +9, -16, +25, …

slide14

n + 1

1

2

3

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 .

4

slide15

This powerpoint was kindly donated to www.worldofteaching.com

http://www.worldofteaching.com is home to over a thousand powerpoints submitted by teachers. This is a completely free site and requires no registration. Please visit and I hope it will help in your teaching.