To find the height of the next square in the sequence, we can observe that each square is similar to the previous one, with a scale factor of 2. This means that the height of each square is twice the height of the previous square.
Starting with a height of 8 cm for the first square, the heights of the next four squares are:
1st square: 8 cm
2nd square: 2 * 8 cm = 16 cm
3rd square: 2 * 16 cm = 32 cm
4th square: 2 * 32 cm = 64 cm
5th square: 2 * 64 cm = 128 cm
The nth square in the sequence will have a height of 8 * 2^(n-1) cm, where n is the position of the square in the sequence.
The figure shows a sequence of squares inscribed in the first-quadrant angle formed by the line y = (1/2)x and the positive x-axis. Each square has two vertices on the x-axis and one on the line y = (1/2)x, and neighboring squares share a vertex. The first (smallest) square is 8 cm tall. How tall are the next four squares in the sequence? How tall is the nth square in the sequence?
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