Topic 7a Homework
1. Consider the expression: T = 2n2 + 1 where T is the total number of tiles and n
represents the figure number starting from n = 1.
a. Use black and red tiles and build the first three figures of the tile sequence
represented by T = 2n2 + 1. Sketch and clearly label the figures. Try to
make them look like “2n2 + 1.”
b. Use algebra pieces to build the nth figure for T = 2n2 + 1. Sketch the nth
figure. Clearly label your diagram. Explain your thinking.
c. How many tiles do you need to build the 18th figure? Explain your thinking.
d. Which figure requires 451 black tiles to build? Explain your thinking and
show your work.
e. Sketch the (n + 1)st figure. Explain your thinking.
f. Two consecutive figures differ by 42 tiles. Which two figures are they?
Explain your thinking and show your work.