May u please halp.

Question

+1

685

3

+179

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.

Guest · Answer 1 · 2020-11-02T03:46:09

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 · Answer 2 · 2020-11-02T03:52:28

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

Melody · Answer 3 · 2020-11-02T09:05:15

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

What did you do yourself before you asked for help?