I'm having some trouble solving this:

$a_n=(a_{n-1})^3\cdot a_{n-2}$



Thanks for any help


Well all I could think of doing with this relation is finding several values and look for any pattern. I got powers of $3$ in the following order: $0, 1, 3, 10, 33, 109, 360, 1189, ... $

Couldn't find any pattern here.


closed as off-topic by user223391, Leucippus, Shailesh, Namaste, Alex Mathers Dec 25 '16 at 0:34

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Hint: Take logs of both sides and let $b_n=\ln a_n$. The resulting recurrence relation in $b_n$ is linear homogeneous. (To make it even simpler, take log base 3.)

  • $\begingroup$ Amazing, thank you. I think I just spent an hour on that $\endgroup$ – Jon Dec 24 '16 at 23:14

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