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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
2 years, 11 months ago

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

Siddhartha Srivastava - 2 years, 11 months ago

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now i know

Nj Ibera - 2 years, 4 months ago

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Proceed,please!

Lawrence Bush - 2 years, 11 months ago

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

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

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

Siddhartha Srivastava - 2 years, 11 months ago

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