what is the 12th term of Fibonacci # and show the solutions

The Fibonacci sequence is a sequence of numbers where each term is the sum of the two preceding ones. The sequence starts with:

\[ F_1 = 1, F_2 = 1 \]

For all terms \( F_n \) where \( n > 2 \):

\[ F_n = F_{n-1} + F_{n-2} \]

To find the 12th term of the Fibonacci sequence, let's calculate each term step by step:

\[
F_1 = 1, \quad F_2 = 1
\]
\[
F_3 = F_2 + F_1 = 1 + 1 = 2
\]
\[
F_4 = F_3 + F_2 = 2 + 1 = 3
\]
\[
F_5 = F_4 + F_3 = 3 + 2 = 5
\]
\[
F_6 = F_5 + F_4 = 5 + 3 = 8
\]
\[
F_7 = F_6 + F_5 = 8 + 5 = 13
\]
\[
F_8 = F_7 + F_6 = 13 + 8 = 21
\]
\[
F_9 = F_8 + F_7 = 21 + 13 = 34
\]
\[
F_{10} = F_9 + F_8 = 34 + 21 = 55
\]
\[
F_{11} = F_{10} + F_9 = 55 + 34 = 89
\]
\[
F_{12} = F_{11} + F_{10} = 89 + 55 = 144
\]

So, the 12th term of the Fibonacci sequence is:

\[
F_{12} = 144
\]

Would you like more details or have any further questions?

### Related Questions:
1. What is the formula for the general Fibonacci term?
2. How can the Fibonacci sequence be applied in nature?
3. What are some real-life applications of Fibonacci numbers?
4. What is the ratio between consecutive Fibonacci numbers, and what does it approach?
5. Can you derive the 20th term of the Fibonacci sequence?

### Tip: 
Fibonacci numbers are closely related to the golden ratio \( \phi \approx 1.618 \). The ratio of consecutive Fibonacci numbers approximates \( \phi \) as the sequence progresses.

Discover how to calculate the 12th term of the Fibonacci sequence with this easy-to-follow guide. Understand the recurrence relation formula, and explore each Fibonacci term up to F12 = 144. Perfect for students in Grades 6-8 learning about sequences and series.

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