One of the most common follow up questions when you are dealing with a sequence is 'Is the number X in this sequence?'.

There are a couple of ways to do this.

**Method 1****:The**** easy spot.**

There are sometimes really easy ways to do this.

**Example 1: **Is the number 275 in the sequence 4, 8, 12, 16, 20....

You should straight away spot that 275 is off and all the numbers in the sequence are even, so it can't be in the sequence.

**Example 2:** Is the number 97 in the 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? 97 can't be in the sequence.

**Method 2: Using the Nth term.**

To use this, we have to remember that n in the nth term is the position. You can't have a number in the 1.5th position.

**Example 3: Is 75 in the sequence 2, 5, 8, 11...**

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

For our sequence this would be 3n - 1

**Step 2**: Make this nth term equal to the number you are looking for (in this case 75) and then solve the equation

3n - 1 = 75

3n = 76

n = 25.3333

Because n isn't a whole number, 75 cannot be in the sequence

**Example 4: Is 224 in the sequence 8, 14, 20, 26...**

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

For our sequence this would be 6n + 2

**Step 2**: Make this nth term equal to the number you are looking for (in this case 224) and then solve the equation

6n + 2 = 224

6n = 222

n = 37

Because n is a whole number, 224 is in the sequence