|
Question |
Answer |
Example |
| 1 |
What is a sequence? |
A set of numbers that are in order
AND
with a rule to find the next number |
2 4 6 8 ....
Is this a sequence?
YES
The numbers are in order
AND
It is easy to see
that the rule to find the next number is
add 2 to the previous number |
| 2 |
Do we always
just add
to get the next number
in a sequence? |
If the numbers are increasing
then we may have to add
OR
we might have to multiply. |
1 2 4 8 ....
In this example
the rule to find the next number is
multiply by 2 |
| 3 |
If the numbers are decreasing
how do we find the rule then? |
Look for the most simple way first
does subtraction work? |
21 18 15 12 ....
Subtraction works here
the rule is
take away 3 to find the next number |
| 4 |
But, what if the numbers are decreasing
and subraction does not work? |
If subtraction does not work
then try division. |
48 24 12 6 ....
Division works here
the rule is
divide by 2 to find the next number |
| 5 |
Will addition, subtraction, multiplication or division
work in all situations? |
There are some situations
where addition will work
but it may not be very easy to see. |
0 1 1 2 3 5 ....
Addition works here
but the rule is
add the last 2 numbers together
to find the next number |
| 6 |
So, as I asked in the last question,
will addition, subtraction, multiplication or division
work in all situations? |
There are some cases
where it is just easier to recognise that
the sequence is made up
of a particular type of number. |
1 4 9 16 ....
We might see that the rule
add 3, add 5, add 7 and so on will work
but it may just be easier if we know
and can recognise
that all of the numbers in the sequence
are square numbers. |