Question: In the Fibonacci Sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, ... which of these numbers

In the Fibonacci Sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, ... which of these numbers are divisible by 2? 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, ... The answer is every third number, and 2 is the third Fibonacci number. How about the ones divisible by 3? 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, ... The answer is every fourth number, and 3 is the fourth Fibonacci number. Could these be just a coincidence? Examine if this pattern goes on forever.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

On December 31, 2023, Stilton Service Companys year-end, the unadjusted trial balance included the following items: Required 1. Prepare the adjusting entry on the books of Stilton Service Company to...

The Fibonacci Sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, ... Is Defined Recursively As Follows: Start With F_0 = 0 And F_1 = 1. Then, Each Number Is The Sum Of Its...

12. In the Fibonacci Sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, ... which of these numbers are divisible by 2? 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610,...

C Project: Fibonacci Numbers Description Step 1. Your will run your program by the command (let the name of executable be Fibon): Fibon N where N is integer larger than 2, and your program generates...

(IN JAVA). Write a Java program that prints the first 30 values in the Fibonacci series. A Fibonacci series begin with 0 and 1. The next number is then found by adding the previous two numbers. The...

In Exercises 97100, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The Fibonacci sequence 1, 1, 2, 3, 5, 8,...

Write a program that, for a given two integer numbers N and X, calculates the sum S = 1 + 1!/X + 2!/X2 + ... + N!/XN 2. Write a program that reads a number N and calculates the sum of the first N...

I. (50%) Fibonacci numbers: In Python tutorial web site, a Fibonacci function is defined as follows >>>def fib (n) # write Fibonacci series up to n """Print a Fibonacci series up to n.""" while a>> #...

Please help me write this in Python language with comments explaining what's happening in the code. 1. The following program calculates the Fibonacci value given a number (let say 50). def...

c programming pls answer all the questions Question 4a Write a C program that counts the total number of characters entered from the keyboard. Hint: Use while loop with gothard. Sample program output...

Consider the spiral with polar equation r = va0 where a is constant. This spiral occurs frequently in flowers because it allows seeds to be arranged in the most efficient way possible. This highly...

Write a shell script to check whether the given string is Palindrome or not.

Strategic Fit and Diversification in Related Businesses Read the overview below and complete the activities that follow. The purpose of diversification is to build shareholder value. Diversification...

Charitable contributions carryover can be carried forward for how long? 5 years forward 3 years backward then 5 forward Indefinitely They cannot be carried back

3) Journalize the following merchandise transactions: A. Sold merchandise on account, $17,300 with terms 2/10, net 30. The cost of the merchandise sold was $12,600. B. Received payment less the...