Based on the pattern, what are the next two terms of the sequence 9, 15, 21, 27, ...?
Let's look at the sequence term by term:
We can deduce that:
We can test this on the
Since this checks out we can say that the sequence is an arithmetic progression with a common diference of 6.
When you are presented with a sequence of numbers which you have to continue, there are different possibilities to consider.....
- Ask yourself whether the numbers are a specific type of number?
If you recognise a that a certain type of number has been given you can easily fill in the next terms.
- Ask whether there is a term-to-term rule which you can use to get from one term to the next.
- This is often by adding or subtracting the same number each time, this gives an Arithmetic Sequence. (A.P.)
- It can be by multiplying or dividing by the same number each time, this gives a Geometric Sequence. (G.P.)
Maybe adding on the previous term gives the next term. This is called a Fibonacci sequence.
Has a rule been given for the
#n^("th") #term? Like #T_n = n^2/(n+1)#?
In this case we have
#9, 15, 21,27 .....#
You should see that the term-to-term rule is "add 6"
So, following this pattern gives the next 2 terms as