Thursday
December 18, 2014

Homework Help: MATH

Posted by Brian on Friday, April 2, 2010 at 12:49pm.

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?

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