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!