what is the 17th term of Fibonacci sequence and show the solutions round off

The Fibonacci sequence is defined as:

\[ F(0) = 0, \ F(1) = 1, \ F(n) = F(n-1) + F(n-2) \ \text{for} \ n \geq 2 \]

To find the 17th term in the Fibonacci sequence, we can calculate it step by step:

\[
\begin{aligned}
F(0) &= 0, \\
F(1) &= 1, \\
F(2) &= F(1) + F(0) = 1 + 0 = 1, \\
F(3) &= F(2) + F(1) = 1 + 1 = 2, \\
F(4) &= F(3) + F(2) = 2 + 1 = 3, \\
F(5) &= F(4) + F(3) = 3 + 2 = 5, \\
F(6) &= F(5) + F(4) = 5 + 3 = 8, \\
F(7) &= F(6) + F(5) = 8 + 5 = 13, \\
F(8) &= F(7) + F(6) = 13 + 8 = 21, \\
F(9) &= F(8) + F(7) = 21 + 13 = 34, \\
F(10) &= F(9) + F(8) = 34 + 21 = 55, \\
F(11) &= F(10) + F(9) = 55 + 34 = 89, \\
F(12) &= F(11) + F(10) = 89 + 55 = 144, \\
F(13) &= F(12) + F(11) = 144 + 89 = 233, \\
F(14) &= F(13) + F(12) = 233 + 144 = 377, \\
F(15) &= F(14) + F(13) = 377 + 233 = 610, \\
F(16) &= F(15) + F(14) = 610 + 377 = 987, \\
F(17) &= F(16) + F(15) = 987 + 610 = 1597.
\end{aligned}
\]

Thus, the 17th term of the Fibonacci sequence is \( 1597 \).

No rounding is necessary since \( 1597 \) is an integer.

Would you like more details on the Fibonacci sequence, or do you have any other questions?

Here are 5 related questions:
1. What is the 20th term of the Fibonacci sequence?
2. Can you calculate the sum of the first 17 Fibonacci numbers?
3. How do you calculate the nth Fibonacci number using a formula?
4. What are the applications of the Fibonacci sequence in nature?
5. Can Fibonacci numbers be extended to negative indices?

**Tip**: Fibonacci numbers can be calculated using an efficient method called "memoization" to speed up the process, especially for larger terms.

Discover how to calculate the 17th term in the Fibonacci sequence using the recurrence relation formula. This detailed step-by-step solution demonstrates the calculation of Fibonacci numbers, a key concept in number theory. Suitable for students in Grades 6-8.

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