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

 

 

Thank you!

 Feb 28, 2021
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Given this recursion equation, we can use the given $a_0=1$ and $a_1 = 5$ conditions to solve for $a_2,$ and then $a_3$. If we first let $n=1,$ we get $$(a_1)^2 - a_0 a_2 = (-1)^1,$$

$$25 - 1(a_2) = -1,$$

$$a_2 = 26.$$

Using this same logic, try to figure out $a_3$ by substituting into the relation $n=2.$

 Feb 28, 2021

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