# Math Help: What Is Extrapolation?

Tools of interpolation and extrapolation can be useful outside of math class. In adult life, people often must extrapolate unknowns based on patterns. It's one of the tools we use to understand other people based on their patterns of behavior. Here are some explanations and tricks to make this math unit a little easier.

### What Is Extrapolation?

Extrapolation in math is the process of finding a value beyond a set of given values. You most often have to use extrapolation when you have to find values in a sequence, or when making graphs. When you use extrapolation, you look for the relationship between the given values. Look at the following sequences. What's the relationship between the values?

• 2, 4, 6, 8…
• 5, 10, 15, 20…

The numbers in the first sequence are increasing by two and the numbers in the second sequence are increasing by five. Now you can use extrapolation to determine the fifth term in each sequence. The fifth term of the first sequence is 10. The fifth term of the second sequence is 25. Linear extrapolation is all about finding patterns in number groups or sequences.

### Interpolation vs. Extrapolation

Interpolation is the process of finding data points located between given points. If you have points on a graph marked (2, 3) and (6, 5), and you are asked to find coordinates for a third point in between the given ones, you could perhaps choose (4, 4). If you're working with number sequences, and are asked to interpolate a missing number between 10, 12, 16 and 18, you could determine that each of the numbers has two digits between it and the next number except between the 12 and 16. By using interpolation, you could guess that the missing number is 14.

The difference between interpolation and extrapolation is that the former is finding an unknown spot within given values while the latter requires extending beyond (or before) the given end points. In a similar example, imagine you were asked to extrapolate the next number in the sequence 10, 12, 14, 16, 18. You could notice that there are two digits between each of the given numbers and identify that the next number would be 20.

### Graphs and Extrapolation

You may have seen problems in your math book that require you to estimate in extrapolating values based on a graph of given points. If the given values create an exponential line, you can estimate the next points by continuing to draw the line in the same direction. Be careful to pay attention to subtle curves or changes in the line's direction because these alter how you extrapolate.

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