# The Layups: Numeric Sequences

We now know the breakdown of math items on the ETAA. By far the easiest of the questions are Numeric Sequences. You need to get all four right. Here’s how.

#### Find the change number

Three of the four questions are what I call “First Order” series. That is, the sequence is determined by adding or subtracting the same number over and over again.

For example, what is the missing number in the following series:

7, 20, 33, 46, 59, ?

If you add 13 to each number, you will get the next number in the series. So the answer is 72.

You can get 3 out of 4 right simply by finding the change number, and extrapolating the next number in the series.

But we want 4 out of 4, so here’s the tricky question:

-43, -25, -10, ___, 11, 17, 20

In this series, the change number, … changes. So to see the pattern in the tricky numeric series questions, you need to …

#### Find the change of the change number

I call these “Second Order” series. Here, the change number goes from adding 18, to adding 15, and so on. Figure out how the change number changes – the change of the change number is −3. It takes a little longer to figure out the answer, but if the change number isn’t constant, that’s the simplest way to find the missing number.

Let’s look at page 57 in the binder.