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3-63.

Given that is the length of the bottom edge of the backward L-shaped figures below, what sequence is generated by the total number of dots in each figure? What is the term, or, of this sequence? The term?

figure 1, 1 dot. figure 2, 2 dots, with 1 dot, on top of, right bottom dot. Figure 3, 3 dots with 2 dots, on top of, right bottom dot. Figure 4, 4 dots, with 3 dots, on top of right bottom dot. Figure 5, 5 dots, with 4 dots, on top of right bottom dot.

Find a rule for the sequence. How does the figure number relate to parts in the shape?

Look at the two legs. One way to see figure 3, for example, is a row of 3 and a column of 2 above it (note: you can't count the dot in the corner twice). How would you analyze figure 4 in the same way?

Now use the idea to analyze the figure. If figure , and figure , what is the number of dots in figure ?

The .

The .