When we are dealing with sequences, it helps to understand what a sequence is.
It is just a set of numbers that follow a rule.
In this activity, we are going to look at linear sequences. These are sequences that are increasing or decreasing by the same amount each time
Example 1: For the sequence 7, 9, 11, 13. Give the next two terms and the rule.
We need to look at the difference for this, the difference is always 2 between the terms and it is going up, so the rule is +2
To get the next two terms, we just apply the rule twice, this will give 15 and 17
Example 2: How many lines will be in the next diagram?
Whenever we have a question like this, where a sequence is drawn instead of given as numbers, our first step is to always turn it into a sequence that contains numbers.
If we just count the lines in each diagram, we get the following sequence...
4, 7, 10, 13
So the rule is +3 and the next diagram will have 16 lines. You might also be asked to draw it (but im sure you can do that!)