Questions from Survey of Mathematics

Q: Determine whether the statement is true or false. Modify each false

Determine whether the statement is true or false. Modify each false statement to make it a true statement. 16 divides 2.

Q: The sum of any six consecutive Fibonacci numbers is always divisible by

The sum of any six consecutive Fibonacci numbers is always divisible by 4. Select any six consecutive Fibonacci numbers and show that for your selection this statement is true.

Q: The greatest common factor of any two consecutive Fibonacci numbers is 1

The greatest common factor of any two consecutive Fibonacci numbers is 1. Show that this statement is true for the first 15 Fibonacci numbers.

Q: Twice any Fibonacci number minus the next Fibonacci number equals the second

Twice any Fibonacci number minus the next Fibonacci number equals the second number preceding the original number. Select a number in the Fibonacci sequence and show that this pattern holds for the nu...

Q: (a) Select any three consecutive terms of a Fibonacci sequence

(a) Select any three consecutive terms of a Fibonacci sequence. Subtract the product of the terms on each side of the middle term from the square of the middle term. What is the difference? (b) Repeat...

Q: Lucas Sequence (a) A sequence related to the Fibonacci sequence

Lucas Sequence (a) A sequence related to the Fibonacci sequence is the Lucas sequence. The Lucas sequence is formed in a manner similar to the Fibonacci sequence. The first two numbers of the Lucas se...

Q: The eleventh Fibonacci number is 89. Examine the first six digits

The eleventh Fibonacci number is 89. Examine the first six digits in the decimal expression of its reciprocal, 1/89. What do you find?

Q: Find the ratio of the second to the first term of the

Find the ratio of the second to the first term of the Fibonacci sequence. Then find the ratio of the third to the second term of the sequence and determine whether this ratio was an increase or decrea...

Q: Draw a line of length 5 in. Determine and mark the

Draw a line of length 5 in. Determine and mark the point on the line that will create the golden ratio. Explain how you determined your answer.

Q: Determine whether the sequence is a Fibonacci type sequence (each term

Determine whether the sequence is a Fibonacci type sequence (each term is the sum of the two preceding terms). If it is, determine the next two terms of the sequence 2, 3, 6, 18, 108, 1944,……