In each progressive figure, one toothpick is added to the top row and one is added to the bottom row. As the #1^"st"# figure has #1# toothpick in the top row and #2# in the bottom row, that means that the #n^"th"# figure will have #n# toothpicks in the top row and #n+1# in the bottom row. Adding these to the #2# toothpicks which constitute the left and right sides, we get the total for the #n^"th"# figure as

#n + (n+1) + 2 = 2n + 3#.

To figure out how many are in the #50^"th"# figure, then, we just let #n=50# to get #2(50)+3 = 103#.