Chapter 9.5, Problem 2P

Assume that the pattern of a circle followed by 3 squares and a triangle continues to repeat in the sequence of shapes in Figure 9.50 and that the numbers below the shapes indicate the position of each shape in the sequence.

1. What shape will be above the number 999? Explain how you can tell.
2. How many squares will there be above the numbers 1 through 999? Explain your answer.
3. Consider the numbers that are below the circles. What kind of sequence do these numbers form: an arithmetic sequence, a geometric sequence. or neither? Why? If it is either an arithmetic sequence or a geometric sequence, give an expression for the Nth entry.
4. Consider the numbers that are below the squares. What kind of sequence do these numbers form' an arithmetic sequence. a geometric sequence, or neither? Why? If it is either an arithmetic sequence or a geometric sequence give an expression for the Nth entry.

 

   Figure 9.50 Repeating pattern of shapes .