Figure 9.52 shows a sequence of figures made of small circles. Assume that the sequence contin-...

  

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Figure 9.52 shows a sequence of figures made of small circles. Assume that the sequence contin- ues by the addition of one circle to each of the 5 "arms" of a figure in order to get the next figure in the sequence. Position Position 2 Position 3 Position 4 Position 5 Figure 9.52 A sequence of figures. a. Find an expression for the number of circles making up the Nth figure in the sequence. Explain why your expression makes sense by relating it to the structure of the figures. b. Will there be a figure in the sequence that is made of 100 circles? If yes, which one? If no, why not? Determine the answer to these ques- tions in two ways: with algebra and in a way that a student in elementary school might be able to. c. Will there be a figure in the sequence that is made of 206 circles? If yes, which one? If no, why not? Determine the answer to these ques- tions in two ways: with algebra and in a a way that a student in elementary school might be able to. Figure 9.52 shows a sequence of figures made of small circles. Assume that the sequence contin- ues by the addition of one circle to each of the 5 "arms" of a figure in order to get the next figure in the sequence. Position Position 2 Position 3 Position 4 Position 5 Figure 9.52 A sequence of figures. a. Find an expression for the number of circles making up the Nth figure in the sequence. Explain why your expression makes sense by relating it to the structure of the figures. b. Will there be a figure in the sequence that is made of 100 circles? If yes, which one? If no, why not? Determine the answer to these ques- tions in two ways: with algebra and in a way that a student in elementary school might be able to. c. Will there be a figure in the sequence that is made of 206 circles? If yes, which one? If no, why not? Determine the answer to these ques- tions in two ways: with algebra and in a a way that a student in elementary school might be able to.