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?

## Comments

Sort by:

TopNewestYes, it is solvable. Also, Hint:- Try solving for a few terms. – Siddhartha Srivastava · 1 year, 8 months ago

Log in to reply

now i know – Nj Ibera · 1 year, 1 month ago

Log in to reply

Proceed,please! – Lawrence Bush · 1 year, 8 months ago

Log in to reply

So the sequence is cyclic every \( 6 \) terms.

Therefore, \( a_{2015} = a_5 = \frac{1}{3} \) – Siddhartha Srivastava · 1 year, 8 months ago

Log in to reply