+0

# Sequence

0
115
1

Given a_0 = 1 and a_1 = 5 and the relation $2a_n - a_{n + 1} a_{n - 1} = (-1)^n$ for n >= 1, find a_3.

Aug 31, 2021

#1
+970
+1

$$2a_1 - a_2a_0 = (-1)^1 \quad \rightarrow \quad 2(5) - a_2 \cdot 1 = -1 \quad \rightarrow \quad a_2 = 11$$

$$2a_2 - a_3a_1 = (-1)^2 \quad \rightarrow \quad 2(11) - a_3 \cdot 5 = 1 \quad \rightarrow \quad a_3 = \boxed{\frac{21}{5}}$$

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Aug 31, 2021