Using DSUM
Using the DSUM function is perhaps the best choice. For this example, we used the range A1:A10 as the range for which we need to sum every nth cell. Enter the word Criteria in cell E1. In cell E2, enter this formula:
=MOD(ROW(A2)-$C$2,$C$2)=0
Select cell C2 and then select Data → Data Tools → Data Validation (pre-2007, Data → Validation). Select List from the Allow: box, and in the Source: box, type: 2,3,4,5,6,7,8,9,10. Ensure that the In-Cell drop-down box is checked and click OK.
Using the MOD function will omit row 1, hence the validation list starts from 2.
In cell C1, enter SUM every.... In any cell after row 1, enter this formula:
=DSUM($A:$A,1,$E$1:$E$2)
In the cell directly above where you entered the DSUM function, enter this:
="Summing Every " & $C$2 & CHOOSE($C$2,"st","nd","rd","th","th","th","th","th","th","th") & " Cell"
Nowall you need to do is choose the desired number from cell C2 and the DSUM function will do the rest.