Need formula to sum range of cells consecutively across a row not duplicating used cells

I have many columns of data on a single row that correspond with each month of the year. I'd like to create a formula that would calculate quarterly totals on a different sheet, and then be able to copy and paste that formula down the row and have it maintain the 3 cell range, however it needs to skip the columns that were used in the previous cell.
Example
Sheet 2 A1 = Sheet 1SUM(A1:C1)
Sheet 2 B1 = Sheet 1 SUM(D1:F1)
Sheet 2 C1 = Sheet 1 SUM(G1:I1), and so on.

I have tried copying and pasting the formula across the row, but it gives me SUM(A1:C1), SUM(B1:D1), SUM(C1:E1),etc. respectively, which is not correct.

Is there a way to create a formula to do this? I tried creating a formula using INDEX, but I just kept getting errors.

Please help.

Thanks