I have an Excel spreadsheet that has 3 separate worksheets in it.

The documents will all be printed together as one large document and I
would like consecutive page numbering throughout the document. So
far, all I can get is page 1-3 of the first worksheet, page 1-4 of the
second, etc.

One way is to use:
File Page Setup Page

Where it says "First page number" type in:
Auto