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@Leon
Where does this wisdom come from?
"However, this formula will not work because AF26:AG26 is not a valid table_array. It only has one row and two columns. You need to have at least two rows and two columns for VLOOKUP to work."
VLOOKUP will work just fine on a 1 row X 2 column range/array. It will even work when the lookup array is only a single cell, though it would be meaningless. but it works!
@Scott5932
When you separate the arguments in a SUM formula with comma's, Excel will ignore cells that contain texts. However, using the plus signs will raise a #VALUE! error if any of the cells contains text.
Since you mention that the cells contents come from a VLOOKUP formula that may return "" (i.e. an empty text string) if no match is found, any of the cells C22 ,C23, C24, C25 or C26 may contain an empty string. If so, that will raise an error.
Now, I have no idea about what you are trying to achieve, but you could re-write the first formula you mention to this:
=SUM(Data!V4,C22:C26)
No need to mention every single cell from C22 to C26 if you want to include all cells in the SUM formula.