Based on the pattern, what are the next two terms of the sequence 9, 15, 21, 27, ...?
2 Answers
Explanation:
Let's look at the sequence term by term:
Notice that:
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.
and
Explanation:
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 termtoterm 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)# ?
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In this case we have
#9, 15, 21,27 .....#
You should see that the termtoterm rule is "add 6"
So, following this pattern gives the next 2 terms as