The triangular numbers are the numbers 1, 3, 6, 10, 15, . . .; the square numbers are the numbers
1, 4, 9, 16, 25, . . . The pentagonal numbers 1, 5, 12, 22, 35, . . .. The geometrical language is
justified by the following diagrams:
a. What are the first five hexagonal numbers? What are the first five septagonal numbers?
What are the first five r-gonal numbers? Give a formula for the nth triangular number.
Give a formula for the nth square number. Give a formula for the nth pentagonal number.
In general, give a formula for the nth r-gonal number.
b. How many numbers can you find that are simultaneously triangular and square? How
many numbers can you find that are simultaneously square and pentagonal?
10. The tail of a giant kangaroo is attached by a giant rubber band to a stake in the ground. A
3 answers