Linear Sequences

AimAimTo find the nth term of a sequence

Mapping Diagrams

2nn21426384

What do you notice?

Mapping Diagrams

2nn21426384

Same difference each timeDifference is 2

Mapping Diagrams

4n - 1n3172113154

What do you notice?

Mapping Diagrams

4n - 1n3172113154

Same differencedifference is 4

Generating a sequence for 2n + 5

TERM1st term

2nd

term3rd

term4th

term5th

term …nthterm2n + 5

•An expression can be used to produce a sequence.

•It is referred to as the nth term

Generating a sequence for 2n + 5

TERM1st term

2nd

term3rd

term4th

term5th

term …nthterm2n + 5

(2 x 1 + 5) = 7

7

Generating a sequence for 2n + 5

TERM1st term

2nd

term3rd

term4th

term5th

term …nthterm2n + 5

(2 x 2 + 5) = 9

97

Generating a sequence for 2n + 5

TERM1st term

2nd

term3rd

term4th

term5th

term …nthterm2n + 5

(2 x 3 + 5) = 11

117 9

Generating a sequence for 2n + 5

TERM1st term

2nd

term3rd

term4th

term5th

term …nthterm2n + 5

(2 x 4 + 5) = 13

11117 9 13

Generating a sequence for 2n + 5

TERM1st term

2nd

term3rd

term4th

term5th

term …nthterm2n + 5117 9 1

513

The sequence generated by 2n + 5 is

7, 9, 11, 13, 15, …….What do you notice?

Generating a sequence for 2n + 5

TERM1st term

2nd

term3rd

term4th

term5th

term …nthterm2n + 5

(2 x 5 + 5) = 15

11117 9 15

13

Generate a sequence for 4n + 3

TERM1st term

2nd

term3rd

term4th

term5th

term …nthterm4n + 3

Generate a sequence for 4n + 3

TERM1st term

2nd

term3rd

term4th

term5th

term …nthterm

7 11 15 19 23 4n + 3

Activity: Complete the sequences

TERM 1st 2nd 3rd 4th 5th …nth

6n – 4 5n + 22n + 7n – 4n + 2

Solutions

n + 276543

n – 410-1-2-3

2n + 7171513119

5n + 2272217127

6n – 4 26201482

nth…5th4th3rd2nd1stTERM

127

What if…..

• We knew the sequence, how could we find the nth term?

Finding the nth term

TERM1st term

2nd

term3rd

term4th

term5th

term …nthterm

8 10 12 14 16

How much is each term increasing by?

Finding the nth term

TERM1st term

2nd

term

3rd

term

4th

term

5th

term …nthterm

8 10 12 14 16

+ 2

+ 2

+ 2

+ 2

Finding the nth term

TERM

1st term

2nd

term

3rd

term

4th

term

5th

term …nthterm

8 10 12 14 16

The common difference is 2.

The nth term begins with 2n

Finding the nth term

TERM1st term

2nd

term3rd

term4th

term5th

term …nthterm

8 10 12 14 16

2 4 6 8 10 2n

The sequence generated by 2n is

Finding the nth term

TERM1st term

2nd

term3rd

term4th

term5th

term …nthterm

8 10 12 14 16

2 4 6 8 10 2n

What would I need to add to the second sequence so that it is equal to the first sequence?

+ ?

+ ?

+ ?

+ ?

+ ?

Finding the nth term

TERM1st term

2nd

term3rd

term4th

term5th

term …nthterm

8 10 12 14 16

2 4 6 8 10 2n

I would need to add 6 to each term

+ 6

+ 6

+ 6

+ 6

+ 6

+ 6

Finding the nth term

TERM1st term

2nd

term3rd

term4th

term5th

term …nthterm

8 10 12 14 162n + 6

2 4 6 8 10 2n

I would need to add 6 to each term

If…..

• The nth term is 5n – 1, how could I find the value of the 100th term?Either I could write out all the terms until I reached the 100th term.

OR

I could substitute n for 100.100th term is (5 x 100) – 1 = 499