# Sequence

Hey,guys i once saw this problem at my national math olympiad ans wanted to know if it is stated right: Consider the infinite sequence defined as : $$a_1=2$$,$$a_2=3$$ and $$a_{k+2}=\frac{a_{k+1}}{a_k}$$ for $$k >= 3$$.Find $$a_{2015}$$.Is it solvable?

Note by Lawrence Bush
3 years, 4 months ago

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Yes, it is solvable. Also, Hint:- Try solving for a few terms.

- 3 years, 4 months ago

now i know

- 2 years, 9 months ago

- 3 years, 4 months ago

$$a_1 = 2, a_2 = 3, a_3 = \frac{3}{2}, a_4 = \frac{1}{2}, a_5 = \frac{1}{3}, a_6 = \frac{2}{3}, a_7 = 2, a_8 = 3$$

So the sequence is cyclic every $$6$$ terms.

Therefore, $$a_{2015} = a_5 = \frac{1}{3}$$

- 3 years, 4 months ago