Unit 1 Pupil Book 5-7 Math Worksheet Page 7
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10.4 Sequences
.4 Sequences
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Generate and describe integer sequences
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Generate and predict terms from practical contexts
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A mathematical sequence is a list of numbers which follow a
rule or pattern. The numbers in a sequence are called the
terms of the sequence.
Level 5
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A term-to-term rule tells you what to do to each term to obtain the next
term in a sequence.
Level 5
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An arithmetic sequence starts with a number, a, and adds on or subtracts
a constant difference, d, each time. The numbers change in
equal-sized steps
Level 5
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To fi nd the rule for a sequence, look at the differences
The Fibonacci
between consecutive terms – the difference pattern.
Level 5
sequence is a set of numbers
which appears all over nature. It can
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Not all sequences have equal-sized steps.
be used to express the arrangement
For example
Level 6
1
4
9
16 …
of a pine cone or how fast some
species reproduce.
3
5
7
Level 5
I can continue or
For each sequence, identify the term-to-term rule and write the next two terms.
generate a
Term-to-term rule: add 3
sequence and use a
3
3
3
term-to-term rule
T he next two terms are 13 + 3 = 16
4
7
10
13
and 16 + 3 = 19
a
11, 15, 19, 23, …
b
19, 16, 13, 10, …
c
5, 6.5, 8, 9.5, …
d
2.5, 2.6, 2.7, 2.8, …
e
2, 4, 8, 16, …
f
1,
1, 1,
1, …
_
1
g
200, 100, 50, 25, …
h
9, 3, 1,
, …
3
Look at these growing rectangles.
a
Draw the next rectangle in the sequence.
b
Write down the number of squares in each rectangle.
c
Does this sequence increase in equal steps?
Describe what is happening each time.
d
How many squares will be in the 5th and 6th rectangles?
The fi rst term of a sequence is 3, and the term-to-term rule is ‘square the
number and add 1’. What are the next two terms in the sequence?
arithmetic sequence
difference pattern
flow chart
10
Getting things in order
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