Two sequences \(A=\{a_0, a_1, a_2,\ldots\}\) and \(B=\{b_0,b_1,b_2,\ldots\}\) are defined as follows:

\(a_0=0, ~a_1=1, ~a_n= a_{n-1} +b_{n-2} \hspace{2mm}\text{for}\hspace{2mm} n\ge2\)

\(b_0=1, ~b_1=2, ~b_n=a_{n-2} +b_{n-1}\hspace{2mm}\text{for}\hspace{2mm} n\ge2\)

What is the remainder when \(a_{50}+b_{50}\) is divided by \(5\)?

Hey, I took the time to write this in LaTeX so yall can read it.

TheGreatestOofman Nov 2, 2020

#1**0 **

Using a computer program, a_{50} leaves a remainder of 1, and b_{50} leaves a remainder of 2, so a_{50} + b_{50} leaves a remainder of 3.

Guest Nov 2, 2020