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Prove this formula for the Fibonacci Sequence
How does one find a formula for the recurrence relation $a_{1}=1,a_{2}=3, a_{n+2}=a_{n+1}+a_{n}?$

How do I go about obtaining a closed formula for Lucas numbers?

The Lucas numbers $ L_n $ are defined by $L_1 = 1$, $L_2 = 3$, and $L_n = L_{n-1} + L_{n-2}$.

I tried looking into it on my discrete math textbook but I'm really confused. Maybe someone can lay out the steps for it?

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marked as duplicate by Gerry Myerson, Guess who it is., Aryabhata, anon, Henry Apr 20 '12 at 6:40

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

1… –  pedja Apr 20 '12 at 6:02
These are two different questions. –  soniccool Apr 20 '12 at 6:03
You can use the techniques in this question. –  Guess who it is. Apr 20 '12 at 6:04
mystycs: The questions are the same. The conditions $L_{n+2}=L_{n+1}+L_n$ and $L_n=L_{n-1} + L_{n-2}$ (with appropriate range for $n$'s$) are equivalent. If you still think that there is a difference, could you explain what difference is there? –  Martin Sleziak Apr 20 '12 at 6:28
The beauty of mathematics is that if you know that 2 apples plus 2 apples is 4 apples, then even though 2 oranges plus 2 oranges is a different question, you can apply what you have learned to solve it. So it is with the current question and the earlier one. –  Gerry Myerson Apr 20 '12 at 6:42