One of the most common questions you will see when we are working with sequences is:

*"Is the number X in this sequence?"*

There are a couple of ways we can work this out:

**Method 1: **The easy spot

**e.g. Is the number 275 in this sequence: 4, 8, 12, 16, 20, ...?**

Straight away we can spot that 275 seems wrong, as all the numbers in this sequence are** even**.

**e.g. Is the number 97 in this sequence: 3, 8, 13,18, 23, ...?**

This one is a bit trickier.

Did you notice that all the numbers in the sequence end in **3 or 8**?

This means that 97 can't be in this sequence.

**Method 2: **Using the nth term

To use this, we have to remember that the 'n' in the nth term refers to the** position**.

Therefore, it is **never** possible to a number in the 1.5^{th} position, only whole numbers.

**e.g. Is 75 in this sequence: 2, 5, 8, 11, ...?**

**Step 1**: Find the nth term of the sequence.

For this sequence, our nth term would be **3n - 1**.

**Step 2**: Make this nth term equal to the number you are looking for and then solve the equation.

3n - 1 = 75

3n = 76

n = 25.3333

Because n isn't a whole number, this means that **75** __ cannot be__ in this sequence.

**e.g. Is 224 in this sequence: 8, 14, 20, 26, ...?**

**Step 1**: Find the nth term of the sequence.

For this sequence, our nth term would be **6n + 2**.

**Step 2**: Make this nth term equal to the number you are looking for and then solve the equation.

6n + 2 = 224

6n = 222

n = 37

Because n is a whole number, **224** ** is **in this sequence.

In this activity, we will use the nth term to confirm if a number does or does not appear in a given sequence. If we can, we will use the 'easy spot' method first in order to save time and effort.