Recurrence relations

What the problems look like

A few statements from this skill. Answers, hints and worked solutions live in the practice session.

1. Warm-up

   A sequence satisfies the linear recurrence $a_n = 7\,a_{n-1} - 10\,a_{n-2}$ for $n \ge 2$. Find the roots of its characteristic equation. Enter both roots, separated by a comma.

2. Warm-up

   A sequence satisfies the linear recurrence $a_n = 8\,a_{n-1} - 15\,a_{n-2}$ for $n \ge 2$. Find the roots of its characteristic equation. Enter both roots, separated by a comma.

3. Warm-up

   A sequence satisfies the linear recurrence $a_n = 10\,a_{n-1} - 24\,a_{n-2}$ for $n \ge 2$. Find the roots of its characteristic equation. Enter both roots, separated by a comma.

Problems shown under their original terms: Generated (template, solver-computed).