Curriculum · Olympiad Topics · Recursive Sequences

Recursive Sequences

Linear recurrences, characteristic roots, and periodicity hunting.

Objectives

Solve linear recurrences
Find and prove periodicity
Translate recursions into closed forms

The full interactive edition of this lesson ships in v1.5. The topic is live everywhere else — the problems below feed your Recursive Sequences mastery now.

Train the topic

●●●○○Define

f(1) = 1

and

f(n) = f(n-1) + n

for

n \ge 2

. What is

f(20)

?AMC 10 style ●●●●○How many ways can a

2 \times 10

rectangle be tiled by

1 \times 2

dominoes?AIME style