MathDB

4

Part of 2019 India PRMO

Problems(2)

Geometry / Computation

Source:

8/11/2019
An ant leaves the anthill for its morning exercise. It walks 44 feet east and then makes a 160∘160^\circ turn to the right and walks 44 more feet. If the ant continues this patterns until it reaches the anthill again, what is the distance in feet it would have walked?
Recursive sequence and divisibility

Source: Prmo 2019 leg 2 P4

8/25/2019
Let a1=24a_1=24 and form the sequence ana_n, n≥2n\geq 2 by an=100an−1+134a_n=100a_{n-1}+134. The first few terms are 24,2534,253534,25353534,…24,2534,253534,25353534,\ldots What is the least value of nn for which ana_n is divisible by 9999?
number theoryPRMO