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Algebra 2HardWhy the Formulas Work

Why the Formulas Work · Hard problem

A sequence is defined by a1=2, a2=3, an=an−1+an−2a_1 = 2,\ a_2 = 3,\ a_n = a_{n-1} + a_{n-2} for n≥3n \ge 3. Find a6a_6.