/
Sequences and Series Number sequences, terms, the general term, terminology. Sequences and Series Number sequences, terms, the general term, terminology.

Sequences and Series Number sequences, terms, the general term, terminology. - PowerPoint Presentation

hondasnoopy
hondasnoopy . @hondasnoopy
Follow
348 views
Uploaded On 2020-06-18

Sequences and Series Number sequences, terms, the general term, terminology. - PPT Presentation

Formulas booklet page 3 In maths we call a list of numbers in order a sequence Each number in a sequence is called a term 4 8 12 16 20 24 28 32 1 st term 6 th term ID: 781170

terms sequence numbers sequences sequence terms sequences numbers term finite infinite called number multiples steps descending enter ascending series

Share:

Link:

Embed:

Download Presentation from below link

Download The PPT/PDF document "Sequences and Series Number sequences, t..." is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.


Presentation Transcript

Slide1

Sequences and Series

Number sequences, terms, the general term, terminology.

Slide2

Formulas booklet page 3

Slide3

Slide4

In maths, we call a list of numbers in order a

sequence.

Each number in a sequence is called a

term

.

4, 8, 12, 16, 20, 24, 28, 32, . . .

1

st

term

6

th

term

Slide5

A

sequence

can be

infinite

. That means it continues forever.

For example, the sequence of multiples of 10,

Infinite and finite sequences

10, 20 ,30, 40, 50, 60, 70, 80, 90

is infinite.

We show this by adding three dots at the end.

. . .

If a sequence has a fixed number of terms it is called a

finite

sequence.

For example, the sequence of two-digit square numbers

16, 25 ,36, 49, 64, 81

is

finite

.

Slide6

A

sequence

can be

infinite

. That means it continues forever.

For example, the sequence of multiples of 10,

Infinite and finite sequences

10, 20 ,30, 40, 50, 60, 70, 80, 90

is infinite.

We show this by adding three dots at the end.

. . .

If a sequence has a fixed number of terms it is called a

finite

sequence.

For example, the sequence of two-digit square numbers

16, 25 ,36, 49, 64, 81

is

finite

.

Slide7

Here are the names of some sequences which you may know already:

2, 4, 6, 8, 10, . . .

1, 3, 5, 7, 9, . . .

3, 6, 9, 12, 15, . . .

5, 10, 15, 20, 25 . . .

1, 4, 9, 16, 25, . . .

Even Numbers (or multiples of 2)

Odd numbers

Multiples of 3

Multiples of 5

Square numbers

1, 3, 6, 10,15, . . .

Triangular numbers

Naming sequences

Slide8

Ascending sequences

When each term in a sequence is bigger than the one before the sequence is called an

ascending

sequence.

For example,

The terms in this ascending sequence increase in

equal steps

by adding 5 each time.

2, 7, 12, 17, 22, 27, 32, 37, . . .

+5

+5

+5

+5

+5

+5

+5

The terms in this ascending sequence increase in

unequal steps

by starting at 0.1 and doubling each time.

0.1, 0.2, 0.4, 0.8, 1.6, 3.2, 6.4, 12.8, . . .

×2

×2

×2

×2

×2

×2

×2

Slide9

Descending sequences

When each term in a sequence is smaller than the one before the sequence is called a

descending

sequence.

For example,

The terms in this descending sequence decrease in

equal steps

by starting at 24 and subtracting 7 each time.

24, 17, 10, 3, –4, –11, –18, –25, . . .

–7

–7

–7

–7

–7

–7

–7

The terms in this descending sequence decrease in

unequal steps

by starting at 100 and subtracting 1, 2, 3, …

100, 99, 97, 94, 90, 85, 79, 72, . . .

–1

–2

–3

–4

–5

–6

–7

Slide10

Describe the following number patterns and write down the next 3 terms:

Add 3

Multiply by -2

15, 18, 21

48, -96, 192

On your calculator type 3, enter,

times -2, enter, keep pressing enter to generate next terms.

Slide11

Slide12

Slide13

Slide14

Slide15

The general term of a sequence.

Slide16

Generate the first 4 terms of each of the following sequences.

Slide17

Using your calculator:

Slide18

Slide19

Defining a sequence recursively.

Example:

Find the first four terms of each of the following sequences

Slide20

Using TI

Nspire

Ctrl T to see a table of values

In a Graph screen select Sequence and enter as shown.

Slide21

Slide22

Defining a sequence recursively. Fibonacci Sequence.

Slide23

Series and Sigma notation.

When we add the terms of a sequence we create a series.

sequence

series

Slide24

Sigma notation (summation)

Slide25

Write in an expanded form first then use GDC to evaluate

.

Slide26

Ex 7A and & 7B from the handout in SEQTA

Exercise 8.1.3 p 268Questions 12, 13