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 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.

Answer 1

Fibonacci Sequence

One of the most famous formulas in Mathematics. Each number in the sequence is the sum of the two numbers that precede it. Called "nature's secret code," and "nature's universal rule." It was first discovered or "invented" by Leonardo Fibonacci. Italian mathematician, who was born around A.D. 1170, was originally known as Leonardo of Pisa.

Answers:

2, 8, 34, 144, 610

3, 21, 144, 987

No. It is not a coincidence since it has a pattern.

Looking on the Fibonacci sequence, if we are to consider the numbers divisible by 5, we will see that 5 is the fifth in the Fibonacci sequence and the numbers divisible by 5 are every fifth of the Fibonacci sequence. This includes 5, 55, 610. The next number is 8 and it is the sixth in the Fibonacci sequence. The numbers divisible by 8 are every sixth of the Fibonacci sequence which include 8 and 144. The same goes for 13 which is the seventh in the Fibonacci sequence. The numbers divisible by 13 are every seventh of the Fibonacci sequence which include 13 and 377. The same goes for all the next terms of the sequence. If the sequence will be continued, the pattern will goes on forever.