Week 21 B Names of sequences and generating sequences

Week 21 B Names of sequences and generating sequences

Names of sequences and generating sequences

• Bronze - To name different types of sequences

• Silver - To generate a sequence using the term-to-term rule

• Gold -To generate a sequence using the nth term

Names of sequences

In maths, we call a list of numbers in order a sequence. Each number in a sequence is called a term. If terms are next to each other they are referred to as consecutive terms. When we write out sequences, consecutive terms are usually separated by commas.

Special Sequences

• 1, 4, 9, 16, 25, 36, 49, 64, 81, 100

• 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000

• 1, 3, 6, 10, 15, 21, 28, 36, 45, 55

• Arithmetic - add or subtract to get from one term to the next

• Geometric - multiply to get from one term to the next

• Quadratic - uses square numbers

• Fibonacci - each term is made by adding the two previous numbers.

Triangular Numbers

• These Triangular Numbers are 1, 3, 6, 10, 15, 21

• The next in the sequence would be 28, 36, 45, 55, 66, 78

• You start with 1, then add 2, then add 3, then add 4 etc.

• Adding consecutive triangles makes a square number

• 1+3 = 4 3+6 = 9 6+10 = 16 10+15 = 25 15+21 = 36 21+28 = 49

Multiple Choice

Is the sequence arithmetic: 78, 785, 7855, 78555, ...

(add or subtract the same number each to get from one tern to the next)

• Yes

• No

Is the sequence arithmetic:

78, 785, 7855, 78555, ...

• No this sequence is not arithmetic

• An arithmetic sequence would go up or down by the same amount from one term to the next.

• The sequence is placing an extra 5 on the end of the number to get from one term to the next - it does not go up by the same amount.

Multiple Choice

Is the sequence 2, 4, 12, 48,... geometric?

(multiply by the same number each to get from one tern to the next)

• yes

• no

Is the sequence 2, 4, 12, 48,... geometric?

• This sequence is not geometric.

• A geometric sequence would multiply or divide by the same amount from one term to the next.

• This sequence is 2 x 2 = 4, 4 x 3 = 12, 12 x 4 = 48

Multiple Choice

What happens when you add consecutive triangle numbers?

• you get the next triangle number.

• you get a square number

• you get a cube number

What happens when you add consecutive triangle numbers?

• Adding consecutive triangles makes a square number

• 1+3 = 4 3+6 = 9 6+10 = 16 10+15 = 25 15+21 = 36 21+28 = 49

Multiple Choice

Which of the following describes a Fibonacci Sequence?

• a sequence which goes up by the same amount from one term to the next.

• to get from one term to the next you multiply by the same number each go

• to get from one term to the next you add the previous 2 terms

Which of the following describes a Fibonacci Sequence?

• Fibonacci - each term is made by adding the two previous numbers. 1, 1, 2, 3, 5

• 1 + 1 = 2 1 + 2 = 3 2 + 3 = 5

Multiple Select

Click on the next three terms in this Fibonacci Sequence.

1, 1, 2, 3, 5, 8...

• 13

• 18

• 21

• 27

• 34

Click on the next three terms in this Fibonacci Sequence.

1, 1, 2, 3, 5, 8...

• The answers are 13, 21, 34 because...

• 5 + 8 = 13

• 8 + 13 = 21

• 13 + 21 = 34

Generaging a term-to-term sequences

• To generate a term to term sequence, we need a starting term and a rule.

• If we have part of a sequence, we need to calculate the rule and apply this to find further terms.

Multiple Choice

Find the term-to-term rule for the following sequence:

2, 6, 10, 14...

• +4

• +5

• +3

• +6

Find the term-to-term rule for the following sequence:

2, 6, 10, 14...

• To get from one term to the next, we add 4.

• The rule is +4

Multiple Choice

Find the term-to-term rule for the following sequence:

3, 8, 13, 18...

• +5

• -5

• +3

• +8

Find the term-to-term rule for the following sequence:

3, 8, 13, 18...

• To get from one term to the next, we add 5

• The rule is +5

Multiple Choice

Find the term-to-term rule for the following sequence:

63, 58, 53, 48...

• -3

• -2

• -4

• -5

Find the term-to-term rule for the following sequence:

63, 58, 53, 48...

• To get from one term to the next, we subtract 5

• The rule is -5

Multiple Choice

Find the term-to-term rule for the following sequence:

19, 16, 13, 10...

• -3

• -2

• -4

• -5

Find the term-to-term rule for the following sequence:

19, 16, 13, 10...

• To get from one term to the next, we subtract 3

• The rule is -3

Multiple Choice

Find the next term in the following sequence:

3, 8, 13, 18...

• 23

• 28

• 20

• 18

Find the next term in the following sequence:

3, 8, 13, 18...

• To get from one term to the next, we add 5

• To find the next term we need to +5 to 18

• The next term is 23

Multiple Choice

Find the next term in the following sequence:

2, 6, 10, 14...

• 18

• 20

• 22

• 16

Find the next term in the following sequence:

2, 6, 10, 14...

• To get from one term to the next, we add 4

• To find the next term we need to +4 to 14

• The next term is 18

Multiple Choice

Find the next term in the following sequence:

20, 17, 14, 11...

• 7

• 6

• 8

• 5

Find the next term in the following sequence:

20, 17, 14, 11...

• To get from one term to the next, we subtract 3

• To find the next term we need to -3 from 11

• The next term is 8

Multiple Choice

Find the next term in the following sequence:

7, 5, 3, 1...

• -2

• -1

• 0

• 1

Find the next term in the following sequence:

7, 5, 3, 1...

• To get from one term to the next, we subtract 2

• To find the next term we need to -2 from 1

• The next term is -1

Generating a sequence from the nth term

The nth term is how we describe a position to term rule, This is a rule which we substitute the position number into a rule to find the term in that position.

If we wanted to find the 3rd term, we would use n = 3. For the 10th term we would use n = 10, and for the 50th term, n = 50.

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Fill in the Blank

A sequence has the n^th term rule 2n

What is the third term? (hint: n = 3)

A sequence has the n^th term rule 2n.

What is the third term?

• To find the third term we use n = 3

• To find 2n we do 2 x 3

• The third term is equal to 6

Fill in the Blank

A sequence has the n^th term rule 2n + 5

What is the fourth term?

A sequence has the n^th term rule 2n + 5

What is the fourth term?

• To find the fourth term we use n = 4

• To find 2n + 5 we do 2 x 4 +5

• The fourth term is equal to 13

Fill in the Blank

A sequence has the n^th term rule -2n + 1

What is the first term?

A sequence has the n^th term rule -2n + 1

What is the first term?

• To find the first term we use n = 1

• To find -2n + 1 we do -2 x 1+ 1

• The fourth term is equal to -1

Multiple Choice

List the first 5 terms of the following sequence: 4n

• 2, 5, 8, 11, 14

• 4, 8, 12, 16, 20

• 9, 11, 13, 15, 17

• 2, 6, 10, 14, 18

Multiple Choice

List the first 5 terms of the following sequence:

4n - 2

• 2, 5, 8, 11, 14

• 4, 8, 12, 16, 20

• 9, 11, 13, 15, 17

• 2, 6, 10, 14, 18

Fill in the Blank

List the first 5 terms of the following sequence:

2n + 7

Fill in the Blank

List the first 5 terms of the following sequence:

3n-1

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