A few sequences…

9, 13, 17, 21….

….. 25, 29term to term rule: add 4

A few sequences…

20, 15, 10, 5….

….. 0, -5term to term rule: minus 5

A few sequences…

1, 10, 100, 1000….

….. 10,000, 100,000term to term rule: x 10

A few sequences…

88, 44, 22, 11….

….. 5.5, 2.75term to term rule: half

Sequencesthe nth term

Level 6 - D grade C / D Level 7 - C grade

generate terms of a linear sequence using term-to-term and position-to-term

rules

generate terms of a sequence using term-

to-term and position-to-term rules

justify generalisations for the nth term of linear

and quadratic sequences

write an expression for the nth term of a simple

arithmetic sequence,

generate sequences from practical contexts and write and justify an expression to describe

the nth term of an arithmetic sequence

10, 20, 30, 40, 50, 60, 70……

1st 2nd 3rd 4th 5th 6th 7th

The position to term rule is:

whichever term I’m

interested inX 10

4, 8, 12, 16, 20, 24, 28……1st 2nd 3rd 4th 5th 6th 7th

The position to term rule is:

whichever term I’m

interested inX 4n

nth term = n x 4

What is the position to term rule:

2, 4, 6, 8, 10 …. nth term =

6, 12, 18, 24 …. nth term = 6n

5, 10, 15, 20, 25…. nth term = 5n

100, 200, 300, 400…. nth term = 100n

What’s the 7th term?

What’s the 10th term?

What’s the 18th term?

n x 2 = 2n

700

1000

1,800

more complicated….

5, 8, 11, 14, 17, 20 …..

+3 +3 +3 +3 +3 common difference is 3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

nth term = 3n + 2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

+ 2

6, 11, 16, 21, 26…

Step 1: Common difference?

nth term = 5n

Step 2: How has the table been shifted?

+ 1

To work out the rule for the nth term of a sequence

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

+ 1

Questions to try:Work out the rule for the nth term then work out the 100th term

a) 3, 5, 7, 9, 11, 13….

b) 12, 20, 28, 36, 44….

c) 19, 29, 39, 49, 59….

d) 7, 10, 13, 16, 19….

e) 14, 20, 26, 32, 38….

f) 55, 60, 65, 70, 75…

g) 8, 17, 26, 35, 44….

!!

Extension:

h) 1, 9, 17, 25, 33….

i) -2, 8, 18, 28, 38….

j) -2, -4, -6, -8, -10…

k) 1, 4, 9, 16, 25….

l) 3, 6, 11, 18, 27….!!

You own a taxi company that charges as follows:

•£3.50 for calling the cab

•20p for every minute of journey time

Real Life Example:

1. Work out a formula for the cost of a journey that’s n minutes long

2. Use your formula to cost a journey of 2 hours

What pattern of matchsticks would follow this sequence rule: 4n + 2

Sequencesthe nth term

Level 6 - D grade C / D Level 7 - C grade

generate terms of a linear sequence using term-to-term and position-to-term

rules

generate terms of a sequence using term-

to-term and position-to-term rules

justify generalisations for the nth term of linear

and quadratic sequences

use expressions to describe the nth term of a

simple arithmetic sequence, justifying its form by referring to the

context

generate sequences from practical contexts and write and justify an expression to describe

the nth term of an arithmetic sequence

Extension work

T(n) = n2

T(n) = 3n2 + n

T(n) = 4n2 + n – 1

• For each of these sequences work out the first five terms• What is the first difference?• What is the second difference?• Is there a way of predicting the second difference?