Let the first 4 terms be A,B,C, and D

A=2, B=7, C=9, D=11

We observe that

2+7=9, 
9+2=11

And the formula for that is 

A+B=C, 
C+A=D

Now A and B become what were previously 
C and D respectively. So A is now 9 and 
B is now 11.

We use the same formula:

A+B=C=9+11=20
C+A=D=20+9=29

So the next two terms are 20 and 29.

So now the sequence is 2,7,9,11,20,29

---

Now A and B become what were previously 
C and D respectively. So A is now 20 and 
B is now 29.

We use the same formula:

A+B=C=20+29=49
C+A=D=49+20=69

So the next two terms are 49 and 69.

So now the sequence is 2,7,9,11,20,29,49,69

---

Now A and B become what were previously 
C and D respectively. So A is now 49 and 
B is now 69.

We use the same formula:

A+B=C=49+69=118
C+A=D=118+49=167

So the next two terms are 118 and 167.

So now the sequence is 2,7,9,11,20,29,49,69,118,167,...

Etc.. etc., etc. 

Note:  There is never just one patteren for a sequence.
This pattern may not have been the pattern your teacher
had in mind but it IS a possible pattern.

Another possibility is 



which gives sequence 2,7,9,11,16,27,47,79,126,191,...

and as you see, is entirely different after the first four terms.


I wonder why they are teaching these sequences of integers
as if there were only one way to continue them.  I would
appreciate it if you would tell me in the thank-you note 
form below what course you are studying and if there is any 
textbook for such a course.
 
Edwin