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# I have no clue how to solve this, can someone help?

Given a positive sequence $$\{ a_n\}$$ where $$a_1=2, a_2=5$$, such that $$a_{n+1}^2=a_n \cdot a_{n+2}+3$$ for all positive integers $$n$$. Does there exist a constant $$b$$ such that $$a_n+a_{n+2}=b \cdot a_{n+1}$$ for any positive integer $$n$$ ? Justify your answer.

Note by Sihfgrty Qhg
6 months, 1 week ago