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Fibonacci extended

Choose two whole numbers (number one and number two). Add them together and form a Fibonacci-like sequence (add number one and number two together to get number three, then add number two and number three together to get number four, etc.). End with a total of ten numbers. Repeat the process by starting with two different numbers.

What is the relationship between the seventh term and the sum of the terms (for each sequence)? What is the relationship between the seventh term and the tenth term (for each sequence)? Explain.

 Extensions
 Would your result be different if you started with negative numbers or fractions?

 Related External Resources
 Fibonacci Numbers and the Golden Section This page discuss applications, real world phenomena, puzzles, patterns, and geometry associated with the Fibonacci numbers and golden section. Fibonacci Online Assessment Take a multiple choice quiz that tests your knowledge about Fibonacci, the Fibonacci sequence, and the golden ratio. Golden Exploration Worksheet This worksheet from Mathematics Teaching in the Middle School leads students to discover the golden ratio by making various measurements and calculations. The Fibonacci Numbers, Pineapples, Sunflowers and The Golden Mean Learn how you can find the Fibonacci's sequence on a pineapple. Math Course on the Fibonacci Numbers - View the series of lecture notes used for a class exclusively about the Fibonacci numbers. A Day at the Arcade Determine how many ways a coin machine can receive money in exchange for a specific number of game tokens.

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