Exercise 10.
Show that \(a_n = 2^n - 5^n\) is also a solution to the recurrence relation \(a_n = 7a_{n-1} - 10a_{n-2}\text{.}\) What would the initial conditions need to be for this to be the closed formula for the sequence?
Show that \(a_n = 2^n - 5^n\) is also a solution to the recurrence relation \(a_n = 7a_{n-1} - 10a_{n-2}\text{.}\) What would the initial conditions need to be for this to be the closed formula for the sequence?