Download COMMON NUMBER PATTERNS

Common Number Patterns
There are many different types of number pattern. They are also
sometimes called sequences or progressions.
Arithmetic Sequences
Arithmetic sequences have a common difference between consecutive
terms:
For example
1 4 7 10 13 16…..
these dots imply that
the series continues
Or
5 12 19 26 33 40 ……
Or
20 18 16 14 12 10 ……
Geometric Sequences
Geometric sequences have a common multiplier between consecutive
terms:
For example
1 3 9 27 81 243…
Or
4 20 100 500 2500 12500 …
Or
8 4 2 1 ½ ¼…
Fibonacci Sequences
Named after an Italian mathematician, Fibonacci sequences have each
term as the sum of the previous two terms:
For example
1 1 2 3 5 8 13 …
Or
1 3 4 7 11 18 29 …
Or
2 5 7 12 19 31 50 …
Other Sequences
And there are sequences based on formulae:
1 4 9 16 25 36 49…
is called the square numbers
1 8 27 64 125 216…
is called the cubed numbers
2 3 5 7 11 13 17…
is the prime numbers
1 4 9 12 17 20 25…
is an alternating sequence (add 3, add 5,
add 3, add 5, etc.)
Examples
Find the next 3 terms of the following sequences:
a.
30 35 40 45 50 …
b.
102 89 76 63 50 …
c.
1458 486 162 54 18 …
d.
4 5 9 14 23 …
e.
4 6 5 7 6 8…
f.
2 5 10 17 26 …
a.
Arithmetic sequence with a common difference of 5
55 60 65
b.
Arithmetic sequence with a common difference of -13
37 24 11
c.
Geometric sequence with a common multiplier of ⅓
6 2 ⅔
d.
Fibonacci sequence
37 60 97
e.
Alternating sequence (add 2, subtract 1, add 2, etc.)
7 9 8
f.
Square numbers plus 1
37 50 65
You might notice that (f) above has differences increasing by 2, and you
could use this to find the next terms, as it is a property of the square
numbers.
These are the sequences that you will be expected to recognise, but there
are many other (sometimes strange) sequences.