echo $(($n + ${arr[i]}))

echo $((n + arr[i]))

The $ or ${..} on regular variables in arithmetic contexts is unnecessary, and can even lead to subtle bugs. This is because the contents of $((..)) is first expanded into a string, and then evaluated as an expression:

$ a='1+1'
$ echo $(($a * 5))    # becomes 1+1*5
6
$ echo $((a * 5))     # evaluates as (1+1)*5
10

The $ is unavoidable for special variables like $1 vs 1, $# vs #. It's also required when adding modifiers to parameters expansions, like ${#var} or ${var%-}. ShellCheck does not warn about these cases.

The $ is also required (and not warned about) when you need to specify the base for a variable value:

$ a=09
$ echo $((a + 1))          # leading zero forces octal interpretation
bash: 09: value too great for base (error token is "09")
$ echo $((10#a + 1))
bash: 10#a: value too great for base (error token is "10#a")
$ echo $((10#$a + 1))
10