Hi. I'm Paul from Romania. I joined this forum because i wanted to share my knowledge and learn from you all.
I have a small problem.
Is there any particular formula to find the general term of a recurrence relation?
I must find it for this one:
an+2=an+1 + 2an
Here is a rather primitive method for this problem.
We have: .
We conjecture that: .
. . (The general term is exponential in nature.)
Then we have: .
The function seems to be: .
Assume that is a linear combination of these two functions.
. . That is: .
We know the first two terms of the sequence:
Add  and : .
Substitute into : .