Sensing in non-volatile memory is performed using bias conditions that are dependent on the position of a selected memory cell within a group of non-volatile memory cells. During sensing, a selected memory cell receives a reference voltage while the remaining memory cells receive a read or verify pass voltage. For at least a subset of the unselected memory cells, the pass voltage that is applied is dependent upon the position of the selected memory cell in the group. As programming progresses from a memory cell at a first end of a NAND string toward a memory cell at a second end of the NAND string, for example, the pass voltage for at least a subset of the unselected memory cells that have already been subjected to programming may be increased. This technique may reduce the effects of an increased channel resistance that occurs as more memory cells are programmed.