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what is the 8th term of the fibonacci sequence of 0, 4, ....?

To find the 8th term of the Fibonacci sequence that starts with \(0, 4, \dots\), we need to first determine the pattern or rule that governs this sequence.

Typically, the Fibonacci sequence is defined such that each term after the first two is the sum of the two preceding terms. However, in this modified sequence:

- The first term is \(0\).
- The second term is \(4\).

Let's denote the sequence as \( F_n \), where:
- \( F_1 = 0 \)
- \( F_2 = 4 \)

For \( n \geq 3 \), each term is calculated as:
\[
F_n = F_{n-1} + F_{n-2}
\]

Now let's calculate the next terms:

\[
\begin{aligned}
F_3 & = F_2 + F_1 = 4 + 0 = 4, \\
F_4 & = F_3 + F_2 = 4 + 4 = 8, \\
F_5 & = F_4 + F_3 = 8 + 4 = 12, \\
F_6 & = F_5 + F_4 = 12 + 8 = 20, \\
F_7 & = F_6 + F_5 = 20 + 12 = 32, \\
F_8 & = F_7 + F_6 = 32 + 20 = 52.
\end{aligned}
\]

Therefore, the 8th term of the Fibonacci sequence is **52**.

Would you like more details or have any questions?

Here are 5 related questions you might consider:
1. How would the sequence change if the first term was different?
2. What is the 10th term of this modified Fibonacci sequence?
3. How can you generalize the nth term of this sequence?
4. How does this sequence compare to the traditional Fibonacci sequence?
5. Can you find the sum of the first 8 terms of this sequence?

**Tip:** When dealing with modified Fibonacci sequences, ensure that you carefully identify the initial terms and apply the Fibonacci rule consistently.

Learn how to calculate the 8th term of a modified Fibonacci sequence that starts with 0, 4. Understand the recurrence relation and formula used to derive each term in this sequence. Suitable for students in Grades 7-9.

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