. Using negative numbers
Add, subtract, multiply and divide positive and negative
integers
Use the sign change key to input negative numbers into a
calculator
Why learn this?
Manipulating negativ
e
numbers is a crucial
skill for
anyone working in fi
nance.
You can understand adding or subtracting numbers by
imagining them on a number line. Level 5
2 ⴙ ⴚ5 ⴝ ⴚ3
⫺4
⫺3
⫺2
⫺1
1 ⴚ ⴚ3 ⴝ 4
0
1
2
3
4
Did you know?
5
If you add a negative number, the result is smaller. So, adding a negative
number is the same as subtracting a positive number. Level 5
If you subtract a negative number, the result is bigger. So, subtracting a
negative number is the same as adding a positive number. Level 5
You can use the sign change key,
into your calculator. Level 5
ⴙ
ⴚ
or (ⴚ) , to enter negative numbers
When you multiply or divide a positive number by a negative number, the
answer is negative. Level 6
The earliest known
written use of negative
numbers is in an Indian
manuscript from the
seventh century CE
– but, confusingly, it
uses ‘ⴙ’ as a symbol to
mean negative!
When you multiply or divide a negative number by a positive number, the
answer is negative. Level 6
When you multiply or divide a negative number by a negative number, the
answer is positive. Level 6
Level 5
I can add and
subtract positive
integers to/from
negative integers
Work out
a ⴚ2 ⴚ 5
b ⴚ8 ⴙ 4
c ⴚ8 ⴚ 4
d ⴚ5 ⴙ 7
e ⴚ5 ⴚ 7
f ⴚ1 ⴚ 1
g ⴚ1 ⴙ 1
h ⴚ3 ⴙ 10 ⴚ 2
I can use the sign
change key
to enter negative
numbers into a
calculator
Use the sign change key on your calculator to help with these calculations.
a ⴚ303 ⴙ ⴚ61
b ⴚ48 ⴚ ⴚ211
c ⴚ13 ⴛ ⴚ5
d ⴚ481.1 ⴜ 28.3
e Hannah’s bank statement shows her balance as ⴚ£585 at the end of
January. In February, she makes a deposit of £1200 and withdraws £725.
What is her bank balance at the end of February?
I can multiply
and divide a
negative number by a
positive number
Work out
ⴚ2 ⴛ 5
4
= –10
a 2 ⴛ ⴚ5
b 3 ⴛ ⴚ4
c ⴚ12 ⴜ 3
d 12 ⴜ ⴚ3
e 15 ⴜ ⴚ5
f 12 ⴛ ⴚ6
g ⴚ24 ⴜ 3
h ⴚ3 ⴛ 12 ⴜ 4
Getting things in order
add
divide
integer
multiply
negative
Level 5
Work out
a 13 ⴚ ⴚ3
e 3 ⴙ ⴚ8
b 4 ⴙ ⴚ5
f ⴚ15 ⴙ ⴚ16
c ⴚ1 ⴙ ⴚ5
g ⴚ2 ⴚ ⴚ2
d ⴚ19 ⴚ ⴚ11
h ⴚ5 ⴙ 11 ⴚ ⴚ2
On Monday night the temperature was ⴚ2°C. By 4.30 a.m. Tuesday, the
temperature had dropped by 4 degrees. At 8 a.m. Tuesday, the temperature
was 1°C.
a What was the temperature at 4.30 a.m.?
I can add or
subtract any
integers
Tip
Use a number line
to help you.
b What was the temperature change between 4.30 a.m. and 8 a.m.?
Work out
ⴚ8 ⴜ ⴚ2
Level 6
=4
a ⴚ5 ⴛ ⴚ3
b ⴚ4 ⴛ 8
c ⴚ20 ⴜ ⴚ5
d 39 ⴜ ⴚ3
e ⴚ11 ⴛ ⴚ7
f 12 ⴜ ⴚ1
g ⴚ9 ⴜ ⴚ9
h ⴚ3 ⴛ ⴚ4 ⴜ ⴚ2
Learn this
Copy and complete.
a 4ⴛ
ⴝ ⴚ16
b
c ⴚ72 ⴜ 8 ⴝ
e ⴚ19 ⴜ
ⴝ ⴚ9.5
I can multiply
and divide any
integers
ⴛ 8 ⴝ ⴚ48
d ⴚ21 ⴜ
ⴝ7
f ⴚ12 ⴛ
ⴝ 60
Find two different pairs of numbers that multiply to make
28 and have a difference of 3.
When multiplying or dividing with two
integers:
• if the signs are the same, the
answer is positive
• if the signs are different, the answer
is negative.
Work out these
ii by evaluating the brackets first, and
ii by expanding the brackets first.
I can evaluate
expressions with
negative numbers and
bracket
Do you get the same solution each time?
ⴚ2 ⴛ (3 ⴙ 5)
ii –2 × (3 + 5) = –2 × 8 = –16
ii –2 × (3 + 5) = –2 × 3 + –2 × 5 = –6 + –10 = –16
a ⴚ3 ⴛ (4 ⴙ 7)
A
b ⴚ2 ⴛ (10 ⴚ 3)
c 5 ⴛ (ⴚ2 ⴙ ⴚ4) d (3 ⴚ ⴚ8) ⴛ 7
Pattern spotting
Copy and continue this pattern to find the answer to 3 ⴚ ⴚ4.
3ⴚ2ⴝ1
3ⴚ1 ⴝ2
3ⴚ0ⴝ…
Write out another pattern to help you work out 5 ⴙ ⴚ3.
B
Power play
(ⴚ1)2 ⴝ ⴚ1 ⴛ ⴚ1 ⴝ 1
Work out
a (ⴚ1)3
b (ⴚ1)4
c (ⴚ1)7
d (ⴚ1)10
e (ⴚ1)17
Look for a rule for the value of (ⴚ1)n, where n is any positive integer.
Write down your rule.
positive
sign
sign change key
subtract
1.1 Using negative numbers
5
.2 Indices and powers
Find square numbers, square roots, cube numbers and cube roots
Write numbers using index notation
Use the square, square root, cube and cube root keys on a
calculator
Understand and use the index laws for multiplication and
Why learn this?
division of numbers in index form
Indices are used in fo
rmulae to
measure the amount
of space in
shapes. Square numb
ers are used to
calculate areas, and
cube numbers
are used to calculate
volumes.
Use the index laws for positive powers of letters
When you multiply a number by itself, you are ‘squaring’ it.
For example 42 ⴝ 4 ⴛ 4 ⴝ 16. 16 is a square number. Level 5
Finding the square root of a number is the inverse, or opposite, of squaring.
___
√16 ⴝ 4 because 42 ⴝ 16. 4 is a square root of 16. Level 5
Watch out!
A positive integer
has two square roots, one
positive and one negative,
square
but by conventi
__ on the
the
√
to
rs
refe
sign
root
positive root only.
53 is ‘five cubed’ which means 5 ⴛ 5 ⴛ 5 ⴝ 125.
125 is a cube number. Level 6
The
____inverse of cubing is finding the cube root.
3
√125 is 5 because 53 ⴝ 125. 5 is the cube root of 125. Level 6
You can write repeated multiplication of numbers using index notation.
4 ⴛ 4 ⴛ 4 ⴛ 4 ⴛ 4 ⴝ 45 and 3 ⴛ 3 ⴛ 5 ⴛ 5 ⴛ 5 ⴝ 32 ⴛ 53. Level 6
There are special rules (or ‘laws’) for working with numbers written using
index notation.
• When multiplying, you add the powers:
Joke!
2
3
2ⴙ3
5
3 ⴛ3 ⴝ3
ⴝ3.
• When dividing, you subtract the powers:
58 ⴜ 54 ⴝ 58 ⴚ 4 ⴝ 54. Level 6 & Level 7
Did you know?
Why are the numbers floating?
Because they’re in-da-seas!
Level 5
Without using a calculator, write these squares and square roots.
___
___
a √64
b √25
c 32
d 112
e √100
f 92
g √1
h √36
i 72
j √25
___
_
I can recall the
first twelve
square numbers and
their square roots
____
___
I can use the
squares I know
to calculate others
mentally
Use the squares you know to mentally calculate these.
15 = 3 × 5, so 152 = 32 × 52 = 9 × 25 = 225
152
a 142
b 162
c 202
A 16th-century writer
suggested that the
4th power should be
called ‘zenzizenzic’,
and the 8th power
should be called
‘zenzizenzizenzic’!
d 212
Estimate these square roots.
Use
calculator to check the exact answer.
__ the square root key on your__
√8 22 = 4 and 32 = 9, so √8 lies between 2 and 3 and is closer
__
to 3.
I can estimate
the square
roots of non-square
numbers
Estimate: √8 = 2.8.
6
__
___
___
___
a √11
b √17
c √32
d √74
Getting things in order
cube
cubed
cube number (e.g. 2 3)
__
3
cube root (e.g. √ 8 )
index (indices)
Level 6
Write these numbers as squares, cubes or powers of 10.
100 = 102 because 10 × 10 = 100
a 8
b 64
c 1000
d 10 000
e 1 000 000
I can give the
positive and
negative square roots
of a number
Work out
___
a √121
b the square roots of 81
c the square roots of 4
d √49
I can use index
notation to write
squares, cubes and
powers of 10
____
Rewrite these using index notation.
a 2ⴛ2ⴛ2ⴛ2ⴛ2ⴛ2ⴛ2ⴛ2
b 3ⴛ3ⴛ3ⴛ3
c 7ⴛ7ⴛ7ⴛ7ⴛ8ⴛ8ⴛ8
d 5ⴛ5ⴛ5ⴛ2
Work out
a 43
___
3
c √27
b 23
I can rewrite
numbers using
index notation
_
3
e √1
d 103
Use the cube numbers you know to mentally calculate these.
a 63
c ⴚ93
b 83
Estimate these cube roots.
__
3
a √9
___
d (0.1)3
____
3
b √21
Tip
0.1 ⴝ 1 ⴜ 10
I can estimate
the cube roots
of non-cube numbers
____
3
c √50
3
d √90
I can use
the index laws
for multiplying and
dividing numbers in
index form
I can use a
calculator to find
squares, square roots,
cubes and cube roots
Simplify, leaving your answers in index form.
a 32 ⴛ 33
b 72 ⴛ 75
c 64 ⴛ 62
d 93 ⴛ 9
e 55 ⴜ 52
f 79 ⴜ 74
g 63 ⴜ 62
h 42 ⴜ 42
Use a calculator to write these in order, smallest first.
3
______
√12 167
182
(ⴚ5)3
___________
___
√182 ⴜ √16
Level 7
Simplify these, leaving your answers in index form.
A
a c6 ⴛ c5
b d8 ⴜ d 2
c z3 ⴛ z4
d t5 ⴛ t3 ⴛ t6
e (r 3 ⴛ r 5) ⴜ r2
f (u9 ⴜ u4) ⴛ u2
B
Squared away
Keith writes the numbers
1 to 16 on cards and
8
1
15
10
begins to lay them out.
Two cards next to each other always add up to
make a square number.
8ⴙ1ⴝ9
1 ⴙ 15 ⴝ 16
15 ⴙ 10 ⴝ 25 etc.
Lay out the rest of the cards so that this rule
continues.
index law
index notation
inverse
power
I can recall the
cubes of 1 to
5 and 10, and their
roots
I can use the
cube numbers
I know to calculate
others mentally
I can use the
index laws
for multiplying and
dividing letters in
index form
Binary
Computers often use binary strings to store and
process information. A binary string uses only
the digits 0 and 1, for example 0011000101.
How many different binary strings are there with
a one digit
b two digits
c three digits?
List them in each case.
d How many different binary strings are there
with n digits?
square number
square root
1.2 Indices and powers
7
.3 Prime factor decomposition
Find the lowest common multiple and the highest common factor
Find and use the prime factor decomposition of a number
Understand and use the index laws for multiplication and division
of numbers in index form
Use the index laws for numbers
Why learn this?
Just like the element
s in
chemistry, prime nu
mbers are
the building blocks
that combine
to make ever y other
number.
The lowest common multiple (LCM) of two numbers is the
lowest number that is a multiple of them both. Level 5 & Level 6
The highest common factor (HCF) of two numbers is the highest number that is
a factor of them both. Level 5 & Level 6
You can write any number as the product of its prime factors.
For example 90 ⴝ 2 ⴛ 3 ⴛ 3 ⴛ 5 or 2 ⴛ 32 ⴛ 5. Level 6
You can use the prime factor decomposition to find the HCF and LCM of two
numbers quickly. Level 6
Did you know?
To multiply powers of the same number, add the indices.
3 ⴛ3 ⴝ3
ⴝ3
4
2
4ⴚ2
To divide powers of the same number, subtract the indices. 3 ⴜ 3 ⴝ 3
ⴝ 32
Level 6 & Level 7
2
2ⴙ4
4
6
Any number to the power zero is 1. For example 30 ⴝ 1, 50 ⴝ 1, 350 ⴝ 1. Level 7
Negative powers can be written as unit fractions or decimals.
1
1
1
For example 10ⴚ1 ⴝ __
ⴝ 0.1, 10ⴚ2 ⴝ ___
ⴝ 0.01, 10ⴚ3 ⴝ ____
ⴝ 0.001. Level 7
10
100
1000
The 20th-century
composer Messiaen
wrote a piece of
music that used
prime numbers to
create unpredictable
rhythms.
Level 5
Find all the factor pairs for these numbers.
a 56
b 72
c 48
I can find all the
factor pairs for
any whole number
d 120
I can find the
HCF of two
numbers
Find the highest common factor (HCF) of these numbers.
a 30 and 42
b 27 and 45
c 18 and 66
d 96 and 144
Find the lowest common multiple (LCM) of these numbers.
7 and 9
Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56,
Multiples of 9:
LCM = 63
a 12 and 20
I can find the
LCM of two
numbers
63 , …
9, 18, 27, 36, 45, 54, 63 , …
b 15 and 25
c 30 and 42
d 33 and 121
Level 6
Find the prime factor decomposition of these numbers.
180
180
Look for a pair of factors, neither
18
3
10
6 2
2 3
8
Getting things in order
5
of which is 1.
Circle the factor if it is a prime number.
Continue until no further factor pairs are possible.
180 = 2 × 2 × 3 × 3 × 5 or 22 × 32 × 5
a 30
b 42
c 72
d 99
factor
highest common factor (HCF)
I can find
the prime factor
decomposition of a
whole number
Tip
Check a prime
tion by multiplying the
orisa
fact
factors back together.
index (indices)
index law
index form
Level 6
Simplify these, leaving your answers in index form.
6
a 4 ⴛ4
b 8 ⴜ8
c 6 ⴛ6
d (4 ⴛ 4 ) ⴜ 4
e 34 ⴛ 35
f 72 ⴛ 73
g 56 ⴜ 54
h 25 ⴜ 22
5
9
3
5
3
5
I can use the
index laws
for multiplying and
dividing numbers in
index form
2
Use prime factor decomposition to find the HCF of these numbers.
Complete prime factor decomposition:
Identify common factors, and multiply them:
42 = 2 × 3 × 7
154 = 2 × 7 × 11
HCF = 2 × 7 = 14
a 30 and 48
d 176 and 350
42 and 154
b 30 and 100
c 180 and 210
I can find the
HCF of two
numbers using
their prime factor
decompositions
Use prime factor decomposition to find the LCM of these numbers.
Complete prime factor decomposition: 84 = 2 × 2 × 3 × 7
308 = 2 × 2 × 7 × 11
Multiply together all the factors but only include overlaps once:
2 × 2 × 3 × 7 × 11 = 924
84 and 308
a 35 and 42
b 30 and 100
c 180 and 810
I can find the
LCM of two
numbers using
their prime factor
decompositions
d 176 and 350
I can prove that
any number to
the power zero is 1
a Write down the value of 23. What is the value of 23 ⴜ 23?
b Use an index law to simplify 23 ⴜ 23.
c What is the value of 20?
Level 7
Work these out, writing your answers as decimals.
a 10 ⴜ 10
3
b 10 ⴜ 10
4
7
10
c 10
ⴚ2
ⴛ 10
I can understand
and use negative
indices
d 10 ⴜ 10
ⴚ1
2
a Use an index law to simplify 22 ⴜ 23.
b What is the value of 2ⴚ1?
c A whole number raised to a negative power is smaller than 1. True or false?
I can use the
index laws to
simplify multiplication
and division
calculations
Use prime factor decomposition to simplify these.
Give your answers in index form.
45 ⴛ 48
45 = 32 × 5 and 48 = 24 × 3
so 45 × 48 = 32 × 5 × 24 × 3 = 24 × 33 × 5
a 24 ⴛ 32
A
b 60 ⴛ 21
c 1500 ⴜ 75
B
Factor line
• Calculate the HCF of 12 and 20.
• Draw a pair of axes and join the points (0, 0) and
(12, 20) with a straight line. How many points
with whole-number coordinates (not including
(0, 0)) does the line pass through? What do you
notice?
• Make a prediction: how many points with wholenumber coordinates (not including (0, 0)) will the
line connecting (0, 0) to (12, 15) pass through?
Test your prediction to see if you are correct.
lowest common multiple (LCM)
d 126 ⴜ 30
prime factor
Highest common formula
Using your answers from Q6 and Q7, or
otherwise, copy and complete this table.
Number a
Number b
30
42
30
100
180
210
HCF
aⴛb
LCM
Write down a formula for the LCM.
Can you explain why it works?
prime factor decomposition
1.3 Prime factor decomposition
9
.4 Sequences
Generate and describe integer sequences
Generate and predict terms from practical contexts
Why learn this?
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
Sequences can descr
ibe in
numbers how things
grow
or develop – from th
e size of
an insec t population
to the
spread of a forest fi
re.
A term-to-term rule tells you what to do to each term to obtain the next
term in a sequence. Level 5
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
Super fact!
To find the rule for a sequence, look at the differences
between consecutive terms – the difference pattern. Level 5
Not all sequences have equal-sized steps.
For example 1
4
9
16 …
ⴙ3
ⴙ5
The Fibonacci
sequence is a set of numbers
which appears all over nature. It can
be used to express the arrangement
of a pine cone or how fast some
species reproduce.
Level 6
ⴙ7
Level 5
For each sequence, identify the term-to-term rule and write the next two terms.
ⴙ3
4
ⴙ3
7
ⴙ3
10
13
Term-to-term rule: add 3
The next two terms are 13 + 3 = 16
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, ⴚ1, 1, ⴚ1, …
g 200, 100, 50, 25, …
h 9, 3, 1, _31 , …
Look at these growing rectangles.
I can continue or
generate a
sequence and use a
term-to-term rule
Watch out!
A term-to-term
rule could contain ‘add’,
‘subtrac t’, ‘multiply’
or ‘divide’.
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 first 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?
10
Getting things in order
arithmetic sequence
difference pattern
flow chart
Which of these sequences are arithmetic sequences?
Copy them and identify the values of a and d
for each sequence.
a
c
b
3, 5, 7, 9, …
1, 4, 9, 16, …
d
10, 7, 4, 1, …
7, 17, 27, 37, …
Write the sequence generated by this flow chart.
Is it an arithmetic sequence?
Start with 4
Is your
answer bigger
than 50?
Add 13
Yes
Level 5
Learn this
In an arithmetic
sequence, a is the
first term and d is the
constant difference
that is added on each
time. If the sequence
is decreasing, d is a
negative number.
STOP
I can recognise
and describe an
arithmetic sequence
I can generate a
sequence from a
flow chart
I can recognise
and describe an
arithmetic sequence
I can generate
a sequence from
a practical context
No
Steph is making some terraced houses out of rods.
a Draw the next picture.
b Copy and complete the table.
Number of houses
Number of rods
1
6
2
3
4
5
6
c Describe this sequence with a term-to-term rule.
d Is this sequence arithmetic? If so, write down the values of a and d.
George wants to model the spread of a forest fire.
He starts by colouring in one square in his book.
The fire will spread to another square if it shares
an edge with a square that is already on fire.
I can predict and
test the next
term in a practical
sequence
a Copy and complete the table.
Term number
Squares on fire
b
c
d
e
f
1
1
2
3
Predict the number of ‘squares on fire’ for the 4th and 5th terms.
Draw the fourth term to test your prediction.
What is happening each time? Explain your answer.
Describe this sequence with a term-to-term rule.
Is this sequence arithmetic? If so, write down the values of a and d.
Copy these sequences and write the next two terms.
A
a 3, 4, 6, 9, …
b 100, 99, 97, 94, …
c 5, 7, 11, 17, …
d 2, 8, 18, 36, …
e 49, 36, 25, 16, …
f 1, 8, 20, 37, …
B
Look and say
A sequence begins like this.
1, 11, 21, 1211, 111221, ...
What is the next number in the sequence?
Hint: There is a clue in the title.
generate
predict
sequence
Level 6
I can continue a
non-arithmetic
sequence
Fired up
George used a square-based system to model a forest
fire in Q7. Repeat his experiment using equilateral
triangles. (You may like to use isometric paper.)
Does the fire spread faster or slower?
What real-world situations might this model?
term
term-to-term rule
1.4 Sequences
11
.5 Generating sequences
using rules
Generate a sequence using a term-to-term rule
Generate a sequence using a position-to-term rule
Why learn this?
Position-to-term rules
can help
you predict future ins
tances of
events that follow se
quences
– such as solar eclip
ses.
The term number tells you the position of that term in the sequence. Level 5
A position-to-term rule tells you what to do to the term number to obtain
that term in the sequence. Level 5 & Level 6
A position-to-term rule can be written in words or in algebra.
For example, 3n ⴙ 5: n is the term number, so to find a term multiply its
term number by 3 and add 5. Level 5 & Level 6
Level 5
Each of the arithmetic sequences below has one mistake. Rewrite the sequence
correctly and identify a (the first term) and d (the constant difference).
a
3, 7, 11, 16, …
b
5, 12, 20, 26, …
c
I can recognise
and describe an
arithmetic sequence
12, 10, 6, 3, …
In an arithmetic sequence, the 3rd term is 15 and the 5th term is 23.
What are the values of a and d for this sequence?
In another arithmetic sequence, the 3rd term is 18 and the 7th term is 10.
What are the values of a and d for this sequence?
Use the position-to-term rules to find the 1st, 2nd, 3rd and 10th terms of these
sequences.
Multiply the term number by 2. When term number = 1, term = 1 × 2 = 2.
When term number = 2, term = 2 × 2 = 4.
When term number = 3, term = 3 × 2 = 6.
When term number = 10, term = 10 × 2 = 20.
a Multiply the term number by 5.
b Multiply the term number by 3 and add 2.
Watch out!
Don’t confuse
term-to-term and
position-to-term rules!
c Multiply the term number by 7 and subtract 4.
d Divide the term number by 2 and add 5.
12
Getting things in order
arithmetic sequence
I can find a term
given its position
and a position-to-term
rule
decrease
generate
Level 6
Use the position-to-term rules to find the 1st, 2nd, 3rd and 100th terms of these
sequences.
I can find a term
given its position
and a position-to-term
rule using positive and
negative numbers
a Multiply the term number by ⴚ3.
b Multiply the term number by 2 and subtract 7.
c Subtract 3 from the term number and then multiply by 8.
d Subtract the term number from 10.
e Divide the term number by 4.
I can find a term
given its position
and an algebraic
position-to-term rule
Use the position-to-term rules to find the 1st, 2nd, 3rd and 7th terms of these
sequences.
5n ⴙ 2
Tip
1st term = 5 × 1 + 2 = 7
2nd term = 5 × 2 + 2 = 12
3rd term = 5 × 3 + 2 = 17
7th term = 5 × 7 + 2 = 37
a 4n ⴚ 3
b 100 ⴚ n
c 7n ⴙ 99
d 6n ⴚ 8
e 3 ⴚ 2n
f nⴜ2
If the number
before n is positive, the
sequence is increasing. If it is
negative, the sequence is
decreasing.
a For each of these position-to-term rules, write the first five terms.
5n ⴙ 7
4n ⴚ 2
6n ⴙ 1
ⴚ3n ⴙ 2
b What do you notice about the term-to-term rule and the position-to-term
rule in each case?
Match each term-to-term definition to a position-to-term definition.
Term-to-term
a Start at 3, add 2 each time.
Position-to-term
Multiply the term number
ii
by 4 and subtract 2.
Tip
Find the first
few terms of each
sequence.
b Start at 4, subtract 3 each time.
Multiply the term number
by ⴚ3 and add 7.
c Start at 2, add 4 each time.
Double the term number and add 1.
I can understand
and use algebraic
position-to-term rules
True or false?
a The sequence 7n produces the multiples of 7.
b Every term in the sequence 2n ⴙ 3 is odd.
c The sequence 5 ⴚ n is a decreasing sequence.
d The sequences 2(n ⴙ 4) and 2n ⴙ 8 are not the same.
e Every term in the sequence 3(100 ⴚ n) is positive.
A
B
Can you digit?
The digits 1 to 8 can be arranged as an arithmetic
sequence of two-digit numbers like this.
12, 34, 56, 78 (start at 12, add 22 each time)
Find another way to arrange the digits 1 to 8 as an
arithmetic sequence of two-digit numbers.
increase
position-to-term rule
sequence
Rows by any other name
Calculate the first five terms of the
sequence with the position-to-term rule
_1 n(n ⴙ 1). By what name are these
2
numbers better known?
term
1.5 Generating sequences
using rules
13