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SMO 2023 Senior Round 1 Question 14

SMO · SMO 2023 Senior Round 1

Question 14

A sequence $a_1,a_2,\ldots$ is defined by
$$a_1=5,\quad a_2=7,\quad a_{n+1}=\frac{a_n+1}{a_{n-1}}\quad\text{for }n\ge2.$$
Find the value of $100\times a_{2023}$.