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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?
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