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# Algebra for Praxis II ParaPro Test Prep Study Guide (page 2)

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### Patterns

The ability to detect patterns in numbers is a very important mathematical skill. Patterns exist everywhere in nature, business, and finance. When you are asked to find a pattern in a series of numbers, look to see if there is some common number you can add, subtract, multiply, or divide each number in the pattern by to give you the next number in the series.

For example, in the sequence 5, 8, 11, 14 … you can add 3 to each number in the sequence to get the next number in the sequence. The next number in the sequence is 17.

Examples

What is the next number in the sequence , 3, 12, 48?

Each number in the sequence can be multiplied by the number 4 to get the next number in the sequence: × 4 = 3, 3 × 4 = 12, 12 × 4 = 48, so the next number in the sequence is 48 × 4 = 192

Sometimes it is not that simple. You may need to look for a combination of multiplying and adding, dividing and subtracting, or some combination of other operations.

What is the next number in the sequence 0, 1, 2, 5, 26?

Keep trying various operations until you find one that works. In this case, the correct procedure is to square the term and add 1: 02 + 1 = 1, 12 + 1 = 2, 22 + 1 = 5, 52 + 1 = 26, so the next number in the sequence is 262 + 1 = 677.

The practice quiz for this study guide can be found at:

Math for Praxis II ParaPro Test Prep Practice Problems

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