# Question #5bc5b

##### 1 Answer

#### Explanation:

The trick to recognizing these **Farey sequences** is to first look at the denominators.

For

The number 3 is the biggest denominator and there are 5 terms.

For

The number 4 is the biggest denominator and there are 7 terms.

The pattern for the denominators of all subsequent Farey sequences should be obvious.

The number of terms is always increased by 2. So, for

The first term is always

It may be easier to see if you let the last term

Last term of

Last term of

Last term of

There is always two more terms shoved in each subsequent Farey sequence. Let

I'll let you explore the "questions to consider" on your own!