Accumulated balance
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I need a column formula for Smartsheet considering the following:
 The first row must fulfill this formula: =BUDGET@row  [AUTHORIZED AMOUNT]@row
 From the second row onwards, it should be like this: =BALANCE1  [AUTHORIZED AMOUNT]@row
How can I do it?
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Answers

You can't do that with a column formula. Column formulas have to be the same formula on ever cell.
However, you can do this by putting the first formula in the first row, then copying your desired formula in cell 2, then copying it down through all of your remaining entries. All new rows should automatically pull the correct formula, as long as they are being added to the bottom of the list.
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Check out the Formula Handbook template!