Sequences
A sequence is a list of numbers which follow
a rule or pattern.
The most simple sequence is
1,2,3,4,5,6,7,8,9, where the numbers go up in ones.
So the pattern or rule for this sequence is add 1 each time
The difference between each number is one
1,3,5,7,9, is an odd number sequence and 4,6,8,10
In these sequences the difference between each number is two
You can have a sequence where the differences follow a pattern
1, 2, 4, 7, 11, 16
a rule or pattern.
The most simple sequence is
1,2,3,4,5,6,7,8,9, where the numbers go up in ones.
So the pattern or rule for this sequence is add 1 each time
The difference between each number is one
1,3,5,7,9, is an odd number sequence and 4,6,8,10
In these sequences the difference between each number is two
You can have a sequence where the differences follow a pattern
1, 2, 4, 7, 11, 16
Differences 1 2 3 4 5
In this the difference increases by 1 each time
The next number would be 22 (increase by 6)
When you are asked to continue a sequence or fill in some missing
numbers in a sequence you have to work out the pattern or rule
of the sequence
1, 4, 9, 16, 25 is a square number sequence
1, 8, 27, 64, 125 is a cube number sequence
3, 6, 9, 12, is when the pattern number is multiplied by 3 each time
There are all kinds of rules
The next number would be 22 (increase by 6)
When you are asked to continue a sequence or fill in some missing
numbers in a sequence you have to work out the pattern or rule
of the sequence
1, 4, 9, 16, 25 is a square number sequence
1, 8, 27, 64, 125 is a cube number sequence
3, 6, 9, 12, is when the pattern number is multiplied by 3 each time
There are all kinds of rules
The nth number
Look at this sequence
Sequence 2, 4, 6, 8, 10 .........?
Pattern number (n) 1, 2, 3, 4, 5 ...........n
The numbers in the sequence are twice the pattern number
So the nth number is 2n
Look at this sequence
Sequence 2, 4, 6, 8, 10 .........?
Pattern number (n) 1, 2, 3, 4, 5 ...........n
The numbers in the sequence are twice the pattern number
So the nth number is 2n
Look at this sequence
Sequence 1, 3, 5, 7, 9 .........?
Pattern number (n) 1, 2, 3, 4, 5 ...........n
The numbers in the sequence are twice the pattern number
less 1
Sequence 1, 3, 5, 7, 9 .........?
Pattern number (n) 1, 2, 3, 4, 5 ...........n
The numbers in the sequence are twice the pattern number
less 1
So the nth number is 2n - 1
Look at this sequence
Sequence 3, 6, 9, 12, 15 .........?
Pattern number (n) 1, 2, 3, 4, 5 ...........n
The numbers in the sequence are 3 times the pattern number
Sequence 3, 6, 9, 12, 15 .........?
Pattern number (n) 1, 2, 3, 4, 5 ...........n
The numbers in the sequence are 3 times the pattern number
So the nth number is 3n
Look at this sequence
Sequence 5, 8, 11, 14, 17 .........?
Pattern number (n) 1, 2, 3, 4, 5 ...........n
The numbers in the sequence are 3 times the pattern number
+2
Sequence 5, 8, 11, 14, 17 .........?
Pattern number (n) 1, 2, 3, 4, 5 ...........n
The numbers in the sequence are 3 times the pattern number
+2
So the nth number is 3n + 1
The rule for finding the nth number is to look
at the difference, use this to multiply
by n (e.g. 2n) then look what needs
to be added or subtracted to make it
fit the sequence
(e.g. 2n + 2) or (3n - 1)
at the difference, use this to multiply
by n (e.g. 2n) then look what needs
to be added or subtracted to make it
fit the sequence
(e.g. 2n + 2) or (3n -
In a square number sequence the nth number is n2
In a cube number sequence the nth number is n3
You can also add and subtract to square and cube
sequences
e.g. 2, 5, 10, 17 the nth number is n2 + 1
and 0, 3, 8, 15 would be n2 - 1
In a cube number sequence the nth number is n3
You can also add and subtract to square and cube
sequences
e.g. 2, 5, 10, 17 the nth number is n2 + 1
and 0, 3, 8, 15 would be n2 -