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Math Prize 2012 Problem 7

Source:

September 24, 2012

Problem Statement

Let f1f_1, f2f_2, f3f_3, ..., be a sequence of numbers such that fn=fn−1+fn−2 f_n = f_{n - 1} + f_{n - 2} for every integer n≥3n \ge 3. If f7=83f_7 = 83, what is the sum of the first 10 terms of the sequence?
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