Concatenate int variable from for loop with string - powershell

Question

I'm passing in possibly four file names: FileName1, FileName2, FileName3, FileName4.
Some may be empty, some not. Because of this I need to check if they are empty before using them. So instead of using four if statements I thought I would just loop through them. How I wanted to do that was like this:
for ($i = 1; $i -lt 5; $i++) {
$FileName = $FileName + $i
Write-Host $FileName
}
So I can get Filename1, FileName2, FileName3, FileName4. Instead I get 1, 1 + 2, etc.
I've also tried $FileName$i, $FileName"$($i)", $FileName + "$($i)".
Any ideas?
EDIT
FileName1, FileName2, FileName3, FileName4 are variables that are passed to the script. They could be FileName1="Budget2018.xlsx", FileName2="MonthlyExpenses.xlx", FileName3="", FileName4="". Or all four variables can contain values ... or just FileName1 can contain a value, etc.
I need to check if they are empty before I continue on processing them. So rather than use 4 if statements to check if they are empty I thought I could loop through them referencing the variables as $Filename$i where $i would be the value 1 to 4. I'm trying to concatenate the two values together to represent the variables that are the parameters.

Answer 1

This produces FileName1, FileName2 etc, but I'm not sure how that squares with "I'm passing in four possible filenames", as there's no list in your script.
For($i = 1; $i -lt 5; $i++){
$FileName = "FileName$i"
Write-Host $FileName
}

Answer 2

If I understand what you want then this should do it:
For($i = 1; $i -lt 5; $i++){
$FileName = 'FileName{0}' -f $i
Write-Host $FileName
}
If you want to define the root portion of the name as a variable then:
$root = 'FileName'
For($i = 1; $i -lt 5; $i++){
$FileName = '{0}{1}' -f $root,$i
Write-Host $FileName
}
Ok, so based on the most recent edit, here is a way to do what I now think you want:
1..4 | %{(ls variable:\$("FileName$_")).value}

Answer 3

If you have a single filename, and you want a list created based off that, you can do something like this:
$FileName = 'test'
$FileList = for ($i = 1; $i -le 4; $i++) { "$FileName$i" }
$FileList
# => test1
# => test2
# => test3
# => test4
But I suspect you have a list of files given your question had "check if null/empty" mentioned in it.