Answer:
the rule will be 7
In this unit we consider how number patterns arise, how to find particular patterns
and finding the formula for a general term in a sequence. Again, this topic is an
important building block in mathematical understanding.
7.1 Multiples
We start by looking at a sequence formed by taking multiples of a particular
number. For example,
3, 6, 9, 12, 15, . . . , . . .
which are the multiples of 3.
7.2 Finding the Next Term
Here we use the given numbers of the sequence to deduce the pattern and hence
find the next term
Example
What are the next 3 numbers in the sequences:
(a) 12, 17, 22, . . .
(b) 50, 47, 44, 41, 38, . . .
Solution
(a) To spot the pattern, it is usually helpful to first find the differences between
each term; i.e.
12 17 22
5 5
So the next term is found by adding 5 to the previous term; this gives 27,
32, 37.
(b) Again we find the difference:
50 47 44 41 38
–3 –3 –3 –3
So the next term is found by taking away 3 from the previous term, giving
35, 32, 29.
