CEMC Euclid, 1998

Algebra Difficulty 3.0 AMC 10/12 Prove it Canada

Consider the sequence $t_1=1$ , $t_2=-1$ and $t_n=\left(\frac{n-3}{n-1}\right)t_{n-2}$ where $n\geq 3$ . What is the value of $t_{1998}$ ?

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