Question

1. What is the approximate ratio between the Fibonacci number 610 and the number 377, which immediately precedes it in the sequence?

2. Taio and Keavy are trying to find the next number in the Fibonacci sequence 0, 1, 1, 2, 3, 5, 8, …. Taio says that the next number is 3, while Keavy maintains that the next number is 13. Who is correct?
3. Use the value of phi = 1.618 to predict the 23rd number in the Fibonacci sequence. The 22nd number in the sequence is 17,711.
4. Neve is examining a tree limb. She notices that the smaller branches spiral away from the larger limb

Answer 1

The ratio between Fibonacci numbers 610 and 377 is approximately 1.618, close to the golden ratio. The next number in the Fibonacci sequence after 8 is 13, and using the golden ratio, the 23rd Fibonacci number is approximately 28,653.

Step-by-step explanation:

The approximate ratio between the Fibonacci number 610 and the number 377 is found using division: 610 / 377 ≈ 1.618, which is close to the golden ratio, commonly denoted by phi (φ).

For the next number in the Fibonacci sequence 0, 1, 1, 2, 3, 5, 8, ..., the correct number is 13, as each number in the sequence is the sum of the two preceding numbers (5 + 8 = 13), so Keavy is correct. Taio's answer of 3 is not correct.

Using the value of phi (φ), which is 1.618, to predict the 23rd number in the Fibonacci sequence, when the 22nd number is 17,711, we can approximate the 23rd number as 17,711 * φ ≈ 28,652.98, which we round to the nearest whole number, so it is approximately 28,653.