What's the 100 term of B,B,F,D,F,B... Sequence?

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.

Discover how to find the 100th term of the sequence B, B, F, D, F, B through modulo arithmetic. This problem involves analyzing repeating sequences and applying modulo operations to determine sequence positions. Suitable for students in Grades 9-12.

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