TITLE: How to solve this recurrence relation $a_{n+2} = \sqrt{a_{n+1}\cdot a_{n}}$?
QUESTION [7 upvotes]: I am trying to solve the recurrence:
$$
a_{n+2} = \sqrt{a_{n+1}\cdot a_{n}}
$$
but here is a problem for me. After few steps I have this:
$$
a_n^2 = a_{n-1}\cdot a_{n-2}
$$
and I don't now what to do further. I can solve a recurrence like that 
$$
a_{n+2} + a_{n+1} - a_n = 5 \cdot 2^n,
$$
but I can't find any information about this case (when I have some degree or
square root in a recurrence).

REPLY [14 votes]: Hint: Let $b_n=\log a_n$ and solve a recurrence for $b_n$.