Math Problem Statement
what is the 17th term of Fibonacci sequence and show the solutions to how to round off
Solution
The Fibonacci sequence is defined by the recurrence relation:
with the initial terms:
To find the 17th term, , we can calculate each term up to the 17th term:
F_1 &= 1 \\ 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 \\ 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{align*}$$ ### The 17th term of the Fibonacci sequence is: $$F_{17} = 1597$$ ### Rounding off: Since $$F_{17} = 1597$$ is already an integer, no rounding is needed. However, if you need to round a number, the steps depend on which decimal place you are rounding to: 1. **Identify the place value** you want to round to (e.g., the nearest whole number, tenth, hundredth). 2. **Look at the digit** immediately to the right of your target place. 3. If that digit is **5 or greater**, round up. 4. If that digit is **less than 5**, round down. For example, if you were rounding the number 1597.456: - **Nearest whole number**: Look at the first decimal (4). Since 4 < 5, round down to 1597. - **Nearest tenth**: Look at the next decimal (5). Since 5 >= 5, round up to 1597.5. Would you like more details or have any questions? ### Related Questions: 1. What is the 20th term of the Fibonacci sequence? 2. How can the Fibonacci sequence be derived using the golden ratio? 3. What is the formula for the nth term in the Fibonacci sequence? 4. How does the Fibonacci sequence appear in nature? 5. What are the applications of Fibonacci numbers in computer science? **Tip:** Understanding how to round numbers correctly is crucial for approximations in mathematical and scientific calculations.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Number Theory
Sequences
Rounding Numbers
Formulas
Fibonacci recurrence relation F_n = F_{n-1} + F_{n-2}
Rounding rules
Theorems
Fibonacci Sequence
Suitable Grade Level
Grades 6-8