During AMC testing, the AoPS Wiki is in read-only mode. No edits can be made.

Difference between revisions of "2021 JMPSC Invitationals Problems/Problem 4"

(Created page with "==Problem== Let <math>(x_n)_{n\geq 0}</math> and <math>(y_n)_{n\geq 0}</math> be sequences of real numbers such that <math>x_0 = 3</math>, <math>y_0 = 1</math>, and, for all...")
 
(Problem)
Line 1: Line 1:
 
==Problem==
 
==Problem==
 
Let <math>(x_n)_{n\geq 0}</math> and <math>(y_n)_{n\geq 0}</math>  be sequences of real numbers such that <math>x_0 = 3</math>, <math>y_0 = 1</math>, and, for all positive integers <math>n</math>,
 
Let <math>(x_n)_{n\geq 0}</math> and <math>(y_n)_{n\geq 0}</math>  be sequences of real numbers such that <math>x_0 = 3</math>, <math>y_0 = 1</math>, and, for all positive integers <math>n</math>,
\begin{align*}
+
 
x_{n+1}+y_{n+1} &= 2x_n + 2y_n,\\
+
<cmath>x_{n+1}+y_{n+1} = 2x_n + 2y_n,</cmath>
x_{n+1}-y_{n+1}&=3x_n-3y_n.
+
<cmath>x_{n+1}-y_{n+1}=3x_n-3y_n.</cmath>
\end{align*} Find <math>x_5</math>.
+
Find <math>x_5</math>.
  
 
==Solution==
 
==Solution==
 
asdf
 
asdf

Revision as of 14:01, 11 July 2021

Problem

Let $(x_n)_{n\geq 0}$ and $(y_n)_{n\geq 0}$ be sequences of real numbers such that $x_0 = 3$, $y_0 = 1$, and, for all positive integers $n$,

\[x_{n+1}+y_{n+1} = 2x_n + 2y_n,\] \[x_{n+1}-y_{n+1}=3x_n-3y_n.\] Find $x_5$.

Solution

asdf

Invalid username
Login to AoPS