+0

+1
46
3
+90

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.

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.

Nov 2, 2020
#2
0

a(50) = It is simply the 50th Fibonacci number =12586269025

b(50) = It is the 52nd Fibonacci number             =32951280099

a(50)  +  b(50) =[12586269025 + 32951280099] mod 5 == 4

Nov 2, 2020
#3
+111546
0

Have you written out the beginning of the sequence of yourself?

What did you do yourself before you asked for help?

Nov 2, 2020