So I have this equation:
$$a_n = −a_{n−1 } + 6a_{n−2}$$
How do I find the solution to this? Everywhere I look, everyone is using some initial conditions to solve it, but I don't get those in my paper, only this equation.
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Well I think some initial terms are necessary for a recurrence. – Vidyanshu Mishra May 18 '17 at 07:48
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For instance $f_n=f_{n-1}+f_{n-2}$ is different when you have different initial terms... – Vidyanshu Mishra May 18 '17 at 07:50
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i don't know anything about that, but i just can't understand i don't have any a_0 = something and a_1 = something etc... – Linexxlol May 18 '17 at 07:52
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That's the problem @Linexxlol. You need initial conditions for a recurrence to proceed AFAIK – Vidyanshu Mishra May 18 '17 at 07:54
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but how does that make sense then, this is a assignment from my university teacher, why would he not give inital conditions? – Linexxlol May 18 '17 at 07:56
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When formulated like this, it means that you take two parameters, namely $a_0$ and $a_1$, and find $a_n$ as a function of $n$, $a_0$, and $a_1$. – TZakrevskiy May 18 '17 at 14:19