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Let a1, a2, a3, \dots be a sequence.  If
a_n = a_{n - 1} - a_{n - 2}
for all $n \ge 3,$ and a1 = 11 and a2 = 7, then find a6.

 May 1, 2024
 #1
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Repeatedly using the recurrence formula with n = 3, 4, 5, 6 gives respectively:

 

\(a_3 = a_2 - a_1 = -4\\ a_4 = a_3 - a_2 = -11\\ a_5 = a_4 - a_3 = -7\\ a_6 = a_5 - a_4 = \boxed{4} \)

 May 1, 2024

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