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Exploring Pascal's Triangle

Intermediate Level

Discussion and Solutions

Working with a partner, study the following array of numbers. What patterns do you see in the arrangement of the numbers? Describe each pattern using words and symbols.

 

As you look for patterns, try to answer the following questions:

  1. Can you predict the next row of numbers?
    1, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1

  2. Is there a pattern in the sums of the numbers in the rows?
    The numbers in the rows all sum to powers of 2

  3. Do any numbers repeat?
    Yes, the rows read the same from left to right as from right to left.

  4. Can you find a pattern in the diagonal numbers?
    Yes, natural numbers and triangular numbers

For More information, read about:

natural numbers
 1, 2, 3, 4, ...		 triangular numbers
 1, 3, 6, 10, ...
powers of 2
 2, 4, 8, 16, ...		 Fibonacci numbers
 1, 1, 2, 3, 5, 8, ...

Questions? Write to the workshop facilitators.

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Math Forum * * * * 28 April 1998