To find the 100th term of the sequence $B, B, F, D, F, B, \dots$, let's first identify the pattern.

The sequence repeats in a cycle. Let's break it down:

1. $B$
2. $B$
3. $F$
4. $D$
5. $F$
6. $B$

The sequence is $B, B, F, D, F, B$ and then it repeats.

This pattern has 6 terms, so the 100th term will be the same as the $(100 \mod 6)$th term.

Now, let's calculate $100 \mod 6$:

$100 \div 6 = 16 \text{ remainder } 4$

So, $100 \mod 6 = 4$.

The 4th term in the sequence is $D$.

Thus, the 100th term of the sequence is $D$.

Would you like any further details or have any questions?

Here are some related questions you might find interesting:

1. What is the 200th term of the same sequence?
2. How would you determine the 500th term of the sequence?
3. Can this sequence be described using a formula?
4. How would you write the sequence as a function of $n$?
5. What is the sum of the first 100 terms if each letter represents a specific number?
6. What is the probability of randomly selecting an $F$ in the first 100 terms?
7. How would the sequence change if a new term were inserted after every 6th term?
8. If the sequence were $B, B, F, D, F, B, D$, what would the 100th term be?

Tip: When dealing with repeating sequences, modulo operations are key to determining the position of any term.