Variable $x$n in arithmetic expansion

Question

I come across this tutorial example, especial the line sum=$(($sum+$x$n)). What does $x$n mean in particular? I suppose $x is referenced but not assigned (undeclared/unset variable), isn't it?

https://linuxhint.com/bash_eval_command/

evaltest3.sh

#!/bin/bash

# Initialize the variable $sum with the value 0
sum=0

# Declare a for loop that will iterate for 4 times
for n in {1..4}
do
# Create four variables using eval command
eval x$n=$n

# Add the values of the variable with $sum
sum=$(($sum+$x$n))
done

# Assign `echo` command with string into a variable
command="echo 'The result of the sum='"

# `eval` command print the sum value using variables
eval $command $sum

Answer 1

(Does not directly answer your question, but offers an alternative)

Since bash arithmetic allows us to provide variables "without using the parameter expansion syntax" [Ref] (i.e. without the $), we can write

for n in {1..4}; do ((sum += n)); done

The advantage is that bash handles empty or unset variables as the number zero.