Difference between revisions of "2000 AMC 12 Problems/Problem 8"

Revision as of 18:20, 4 January 2008

Problem

Figures $0$ , $1$ , $2$ , and $3$ consist of $1$ , $5$ , $13$ , and $25$ non-overlapping squares. If the pattern continued, how many non-overlapping squares would there be in figure $100$ ?

$\text {(A)}\ 10401 \qquad \text {(B)}\ 19801 \qquad \text {(C)}\ 20201 \qquad \text {(D)}\ 39801 \qquad \text {(E)}\ 40801$

Solution

By counting the squares starting from the center of each figure, the figure 0 has 1 square, the figure 1 has $1 + 4(1)$ squares, figure 2 has $1+4(1+2)$ squares, and so on. Figure 100 would have $1 + 4(1 + 2 + \cdots + 100) = 1 + 4 \frac{100(101)}{2} = 20201 \Rightarrow \mathrm{(C)}$ .

2000 AMC 12 (Problems • Answer Key • Resources)
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Difference between revisions of "2000 AMC 12 Problems/Problem 8"

Revision as of 18:20, 4 January 2008

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Solution

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