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Let a_1, a_2, a_3, \dots be a sequence. If
a_n = a_{n - 1} + a_{n - 2}
for all n \ge 3, and a_{11} = 4 and a_{10} = 1, then find a_6.

 Feb 20, 2024
 #1
avatar+394 
+1

\(a_{11}=a_{10}+a_{9}\), so following this logic.

\(4=1+a_{9}\)

\(a_{9}=3\)

Similarly,

\(1=3+a_{8}\)

\(a_{8}=-2\)

\(3=-2+a_{7}\)

\(a_{7}=5\)

\(-2=5+a_{6}\)

\(a_{6}=-7\).

a6 is -7.

 Feb 21, 2024

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