Find a particular solution to the recurrence relation an = 9an-1 - 20an-2 + 5n
You asked:
Investigate the equation: \(a n = 9 a n - 1 - 20 a n - 2 + 5 n\).
MathBot Answer:
The graph of the equation \(a n = 9 a n - 1 - 20 a n - 2 + 5 n\) is a hyperbola.
The coordinates of its foci are: \(\left(\frac{5}{12} - \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)\) and \(\left(\frac{5}{12} + \frac{\sqrt{2}}{2}, - \frac{\sqrt{2}}{2}\right)\).
The coordinates of its vertices are: \(\left(- \frac{1}{12}, \frac{1}{2}\right)\) and \(\left(\frac{11}{12}, - \frac{1}{2}\right)\).
The asymptotes have equations: \(5 - 12 a = 0\) and \(n = 0\).