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If a sequence follows a rule :

$a_n=a_{n-1}+a_{n-2}$ for $n\geq3$

$a_1$ and $a_2$ are constants.

I tried finding via method of difference then i found that its difference is also coming out to be same sequence. This is the only method i know of finding general term.

So is there any more method of finding general term.

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  • $\begingroup$ Is $$a_0$$ and $$a_1$$ given? $\endgroup$ Feb 9 '19 at 12:44
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    $\begingroup$ Have you heard of the Fibonacci sequence? $\endgroup$
    – lightxbulb
    Feb 9 '19 at 12:49
  • $\begingroup$ nope. Actually this was the relation which came in a question of finding the way to place n places with heads such that there are no consecutive heads $\endgroup$
    – Amir RAZA
    Feb 9 '19 at 12:50
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    $\begingroup$ Well look it up. $\endgroup$
    – lightxbulb
    Feb 9 '19 at 12:53
  • $\begingroup$ Read it but this is far beyond my current syllabus. I'm undergraduate. Haven't appeared for college yet. $\endgroup$
    – Amir RAZA
    Feb 9 '19 at 12:55
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Hint: Make the ansatz $$a_n=q^n$$ you will get $$q^n=q^{n-1}+q^{n-2}$$

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  • $\begingroup$ I didn't get that $\endgroup$
    – Amir RAZA
    Feb 9 '19 at 12:45
  • $\begingroup$ Why this question has been downvoted.. $\endgroup$
    – Amir RAZA
    Feb 9 '19 at 12:46
  • $\begingroup$ Ok i will try again with your hint $\endgroup$
    – Amir RAZA
    Feb 9 '19 at 12:49
  • $\begingroup$ Can you proceed till end. Cuz I don't hace any knowledge about Fibonacci sequence nor i have read any related concepts. $\endgroup$
    – Amir RAZA
    Feb 9 '19 at 13:27

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