The Arithmetic Reasoning (AR) subtest of the ASVAB often includes questions that test your ability to name what comes next in a sequence of numbers. Generally, these problems are the only AR questions that aren’t word problems. However, sequence questions do test your ability to do arithmetic and to reason, because you have to determine how the numbers relate to each other. And to do this, you must be able to perform mathematical operations quickly.

Suppose you have a sequence of numbers that looks like this: 1, 4, 7, 10, ? Each new number is reached by adding 3 to the previous number: 1 + 3 = 4, 4 + 3 = 7, and so on. So the next number in the sequence is 10 + 3 = 13, or 13.

But of course, the questions on the ASVAB aren’t quite this simple. More likely, you’ll see something like this: 2, 4, 16, 256, ? In this case, each number is being multiplied by itself, so 2 × 2 = 4, 4 × 4 = 16, and so on. The next number in the sequence is 256 × 256, which equals 65,536 — the correct answer.

You may also see sequences like this: 1, 2, 3, 6, 12, ? In this sequence, the numbers are being added together: 1 + 2 = 3, and 1 + 2 + 3 = 6. The next number is 1 + 2 + 3 + 6 = 12. So the next number would be 24.

## Finding the pattern

To answer sequence questions correctly, you need to figure out the pattern as quickly as possible. Some people, blessed with superior sequencing genes, can figure out patterns instinctively. The rest of the population has to rely on a more difficult, manual effort.

Finding a pattern in a sequence of numbers requires you to think about how numbers work. For instance, seeing the number 256 after 2, 4, 16 should alert you that multiplication is the operation, because 256 is so much larger than the other numbers. On the other hand, because the values in 1, 2, 3, 6, 12 don’t increase by much, you can guess that the pattern requires addition.

## Dealing with more than one operation in a sequence

Don’t forget that more than one operation can occur in a sequence. For example, a sequence may be “add 1, subtract 1, add 2, subtract 2.” That would look something like this: 2, 3, 2, 4, ?

Because the numbers in the sequence both increase and decrease as the sequence continues, you should suspect that something tricky is going on.

Make sure to use your scratch paper! Jot down notes while you’re trying to find the pattern in a sequence. Writing your work down helps you keep track of which operations you’ve tried.