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Algebraic Sense
Lesson 19		 Patterns and Functions
  Objectives/Vocab/Tips > Examples 1 | 2 | 3 | 4 > Practice: 1 | 2 | 3 > Reflection

Example 2:

The ancient Greeks discovered that certain numbers form definite shapes when arranged in dot patterns. For example, square numbers have the same number of columns and rows.

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25

Which 3 numbers would come next in this pattern of square numbers?
  1. 36, 49, 64
  2. 49, 64, 81
  3. 36, 64, 100
  4. 49, 81, 121

There are a couple of steps in solving this problem. Let's begin solving this problem by looking at the three arrangements and numbers we are given.

You are told that the numbers have the dot pattern with the same number of columns and rows. You should also notice as well, that the three patterns you are given, go from 1 row 1 column to 3 rows 3 columns and finally 5 rows 5 columns. Notice how the number of rows and columns are consecutive odd numbers. If you were to finish the next three by looking at 1, 3, and 5, you know that the next three will be 7, 9, and 11.

You have found the first half of the solution to this problem. Now all you need to do is to square or multiply each of the three numbers by the same number.

7 x 7 = 49
9 x 9 = 81
11 x 11 = 121

You have now found the next three numbers in this pattern of square numbers. As you look over your choices you notice that letter D, has the three numbers you came up with. Excellent!

The final answer for this problem is letter D, 49, 81, 121.

 

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