The Fibonacci sequence is a well-known mathematical sequence through which the primary two phrases are 1 and 1 after which every time period after that’s discovered by including the earlier two phrases. The primary 10 phrases are proven within the determine under:

It’s a naturally occurring phenomena in nature that was found by Leonardo Fibonacci. Leonardo was an Italian mathematician who lived from about 1180 to about 1250 CE.

Mathematicians right this moment are nonetheless discovering attention-grabbing method this collection of numbers can describe nature. To see how this sequence describes nature, take an in depth have a look at the determine above.

This spiral form is discovered in lots of flowers, pine cones, and snails’ shell to say only a few.

What precisely is occurring right here so far as math is worried? You may see that we start with two squares with a aspect size that is the same as 1.

Then, to get the aspect size of the third sq., we add the aspect lengths of the 2 earlier squares that’s 1 and 1 (1 + 1 = 2)

To get the aspect size of a fourth sq., we add 1 and a pair of (1 + 2 = 3)

To get the aspect size of a fifth sq., we add 2 and three (2 + 3 = 5)

If we proceed this sample we get:

Here’s a quick listing of the Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233

As already acknowledged, every quantity within the sequence is the sum of the 2 numbers earlier than it.

We are able to attempt to derive a Fibonacci sequence system by making some observations.

F1 = 1

F2 = 1

F3 = F2 + F1 = 1 + 1 = 2

F4 = F3 + F2 = 2 + 1 = 3

F5 = F4 + F3 = 3 + 2 = 5

F6 = F6-1 + F6-2 = F5 + F4 = 5 + 3 = 8

F7 = F7-1 + F7-2 = 8 + 5 = 13

……

……

……

Fn = Fn-1 + Fn-2

The recursive system for the Fibonacci sequence is Fn = Fn-1 + Fn-2  with F1 = 1 and F2 = 1

The best way to discover the sum of the primary ten phrases of the Fibonacci sequence

1 + 1 + 2 + 3 + 5 + 8 + 13 + 21 + 34 + 55 = 143

Now, we are going to select numbers apart from 1 and 1 to create different Fibonacci-like sequences

2, 2, 4, 6, 10, 16, 26, 42, 68, 110

The sum is 2 + 2 + 4 + 6 + 10 + 16 + 26 + 42 + 68 + 110 = 286

what if we begin with 3 and three?

3, 3, 6, 9, 15, 24, 39, 63, 102, 165

3 + 3 + 6 + 9 + 15 + 24 + 39 + 63 + 102 + 165 = 429

Now, we will make a pleasant commentary?

143/11 = 13

286/11 = 26

429/11 = 39

143 = 11 × 13 = 11 × 13 × 1

286 = 11 × 26 = 11 × 13 × 2

429 = 11 × 39 = 11 × 13 × 3

You may thus see that the sum of the primary 10 phrases observe this sample

11× 13 × 1

11× 13 × 2

11× 13 × 3

11× 13 × 4

……

……

……

11× 13 × 4

11 × 13 × n

Simply do not forget that n = 1 is the Fibonacci sequence beginning with 1 and 1

n = 2 is the one beginning with 2 and a pair of

And so forth….

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