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
