In A1 of your new sheet, put this:
=OFFSET(Sheet1!$A$1,(ROW()-1)*7,0)
… and copy down. If you start somewhere other than row 1, change ROW() to ROW(A1) or some other cell on row 1, then copy down again.
If you want to copy the nth line but multiple columns, use the formula:
=OFFSET(Sheet1!A$1,(ROW()-1)*7,0)
This can be copied right too.