The other tutor used a difference table.
Here's a different approach which gives the same next term.

Start with--------2
     add  7, get  9
subtract  4, get  5 
     add  8, get 13
subtract  3, get 10
     add  9, get 19
subtract  2, get 17

So it looks like the pattern is: 

1. We alternate between adding and subtracting
2. The numbers we add go 7,8,9,etc
3. The numbers we subtract go 4,3,2,etc.
 
The next thing to do is to add, and the next number to add is 10,
so we have:

Start-------------2
     add  7, get  9
subtract  4, get  5 
     add  8, get 13
subtract  3, get 10
     add  9, get 19
subtract  2, get 17
     add 10, get 27

Edwin