1) In figure 4, the area of the square os 16cubes. The shaded part is 7cubes, being one less than 4^2 or 4*4. The formula is n+n-1. This can be put in for 5 too. 5+5-1=9.
2) Using the formula, 50+50-1=99. Therefor, the shaded squares in the 50th figure would be 99.
Complete sentence:
1) The formula for the number of shaded squares in the Nth figure is n+n-1.
2) There would be 99 shaded squares in the 50th figure.
explanation: Knowing that the area of a square is length*width, in this case because the figures are squares, the length and the width are both the same number. From this, we can tell that for figure 45, the length is 45 and so this the width. The one square in the corner is both the length and the width so this is why we take 1 away or -1.