## Introduction

#link to Lecture Slides

drive.google.com/file/d/1VNK_edNOXOnDm2D5FyMGtNSVOywk9fIU/view

## Content

Fibonacci sequence.

So.

This algorithm, we are going to talk about how to generate the numbers of the Fibonacci sequence.

So.

If you look at this particular pattern here, this is known as the Fibonacci sequence.

So.

The only two are the starting numbers of this sequence happen to be zero and one.

The.

Next number one is the sum of the previous two numbers.

So.

Zero, plus one is one.

Now.

One, plus one is two.

Two, plus one is three.

Three, plus two is five.

Five, plus three is eight.

Eight, plus 5 is 13 13, plus eight is 21.

So.

This particular thing keeps on proceeding forever.

There is no end to the Fibonacci sequence.

Now.

What this algorithm is expecting us to do is, given this first and second, it's expecting us to generate this particular pattern till the end point, specified.

So.

Suppose n is just eight, I will be printing.

0 1 1 2, 3 5, 8.

So, in order to generate this particular pattern.

It is very important to first understand how this sequence is being generated.

So.

What I'll do is I'll call this zero as the first number.

This one as the second number.

And, how I'm getting calculating next, next happens to be first plus second.

So it is zero.

Plus one is one.

Now, in order to calculate two.

What I need to do is I need to move first to second and second to next.

So.

First, what is going to happen is,? The value of second will get copied to first.

Then the value of the current next will get copied to second.

And.

The new next will be calculated as first plus second, which happens to be one plus one, which is two.

Now.

How long should we generate these numbers as long as the value of next is less than or equal to n.? So, n is the endpoint we are going to generate.

So, let's, try to take a look at this body.

So.

What we're trying to do here.

Is, I am copying the value of second to first, then I'm, copying the value of next to second, and I'm calculating next as first plus second, how long do I do it? I do it as long as the value of next is less than or equal to n.

So.

This is a while loop which keeps on happening till I reach the value of n that is next becomes equal to n.

Now.

Let us first go about trying to develop this logic.

And.

Then we'll, go ahead and do the testing as usual.

So before I, even go ahead and do the remaining part of the logic.

Let me try to explain what are these variables.

If.

You see zero happens to be first one happens to be second.

Next is going to be first plus second., In order to generate this particular pattern, I need to know what is the end point or n.

So? What I'm going to say is I'm going to ask the user enter the value of n.

Now in this do while loop or the while do loop, I'm going to keep generating this pattern as long as the value of next happens to be less than or equal to N.

So the first thing what I'm doing is take a look here.

So.

What I am doing now is I.

Am I am first printing zero.

Then I am printing one.

And then I'm entering into a loop, let's say next is also one, and N is just eight.

So.

One is less than or equal to eight is true.

So I'm.

First, writing, next., So.

The next one is also printed.

Now.

It is quite easy.

And I'm, moving the value of second to first and the current value of next into second.

And.

Then I'm saying next is now first plus second.

So.

Next is now 2 is to less than or equal to eight Yes.

So, I am writing 2.

So next 2 is printed here.

Now.

First is one second is also one.

So Second, the value of second, which is one most to first, the value of next, which is 2 move into second.

So.

This is one.

This is two.

So this is one plus two is three.

Next is three.

So.

Now, if you see three is less than or equal to eight.

This condition is true.

Three is printed.

Now.

What happens is two moves into first three moves into second.

Okay.

Two, plus three is five.

Next is five.

Five is less than or equal to eight is true.

I'm going to print five.

This particular thing will continue till the value of next reaches 13.

At that point.

This loop is going to fail because the condition is not true.

And once I come out, I'm just required to stop.

Now in order to understand the working of this particular logic.

We will just go through test run.

So using a test run.

We are able to very easily verify whether the working of a given algorithm or a flowchart in future happens to be correct or not.

So, first is zero.

Second is one.

Next is one, I've asked the user has entered the value of n as 8.

Once the user enters the value of Nas 8 .

Then what am I supposed to do? Is I am going to write first and second so on the , output zero is written.

One is written.

Okay.

So first zero gets written.

Then next one gets written., All right.

Now what is happening is, I need to get into this while loop? Next is one is one less than or equal to eight, two.

So.

What I'm going to do is I am going to write one, this one is written here., All right.

This.

Next one is written here.

Now.

What I'm doing here is I.

Am moving the value of second to first.

So.

Second was one first also now has become one.

Next was one.

Okay.

Second also.

Now, this one is moved from next to second.

Second actually has not changed, but first has changed.

Now.

Next is first plus second.

So it is 2, twois less than or equal to eight, two, so I'm going to print, two., Okay., Now, again.

What I do is I, go ahead and I move these numbers.

This fellow here.

And this fellow here.

So first is again.

One second has taken the value of next, which is to next is one plus two is three.

Three is less than or equal to eight is true., So I'm going to print three.

Then what happens is, at this step, I am going to continue the moment, again, like this.

So.

If you draw arrows like this, it's, very easy to develop the logic and understand what is happening, you need to understand that.

The order of this moment should be in the right step.

You cannot do second is next first and then say, first is second.

Then the whole thing goes for toss, that is the fundamental rule of algorithm doing the steps in the right sequence or right, order.

Okay.

So now what I'm doing is 2 is going to first Okay, and three is going to second, since this is going next is two plus three is five.

Five is less than or equal to eight is true.

So I.

Am printing five.

Then I come here, in the next step.

First becomes three.

Second becomes five.

Next becomes eight.

Eight is equal to eight.

So.

Still we are okay.

So.

We are printing eight.

Then we come back here.

This fellow goes here.

This fellow goes here, whereas next becomes five plus eight or eight, plus five is 13.

13 is not definitely less than or equal to eight, this loop, fails and I come in stop.

If.

You want to understand the working of this, take a larger value of n like 35 60 run through the logic.

Most important point.

This sequence is very important.

Second should first go to first.

Next should then go to second.

If.

You interchange.

The order of these steps, your whole output is going to be a mess.

So.

That is what requires a little thinking or a little logic in writing and a algorithm.

Or flowchart.

The order of steps is absolutely absolutely important, because that's all there is left to logic.

## FAQs

### Is 1 1 2 3 5 8 13 21 35 a Fibonacci sequence? ›

The Fibonacci sequence is **a series of numbers where a number is the addition of the last two numbers, starting with 0, and 1**. The Fibonacci Sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55… This guide provides you with a framework for how to transition your team to agile.

**What is the sequence 1 2 3 5 8 13 21? ›**

**The Fibonacci sequence** is a famous group of numbers beginning with 0 and 1 in which each number is the sum of the two before it. It begins 0, 1, 1, 2, 3, 5, 8, 13, 21 and continues infinitely.

**What are the first 15 Fibonacci numbers 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610? ›**

Fibonacci Sequence List. The list of first 20 terms in the Fibonacci Sequence is: **0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181**.

**How do you write an algorithm for Fibonacci sequence? ›**

**Fibonacci Series Program In C**

- Algorithm. Algorithm of this program is very easy − START Step 1 → Take integer variable A, B, C Step 2 → Set A = 0, B = 0 Step 3 → DISPLAY A, B Step 4 → C = A + B Step 5 → DISPLAY C Step 6 → Set A = B, B = C Step 7 → REPEAT from 4 - 6, for n times STOP.
- Pseudocode. ...
- Implementation. ...
- Output.

**What is the sequence 1 2 3 4 5 8 13 21 34? ›**

**The Fibonacci sequence** begins with the following 14 integers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233 ... Each number, starting with the third, adheres to the prescribed formula. For example, the seventh number, 8, is preceded by 3 and 5, which add up to 8.

**What is the pattern of 1 1 2 3 5 8 13 21 34 55? ›**

**The Fibonacci sequence** is the series of numbers where each number is the sum of the two preceding numbers. For example, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, …

**What is the next number in the sequence 2 3 4 6 6 9 8 12 10? ›**

Therefore, the next number will be **15**. Hence, the correct answer is 15.

**What is the pattern of 1 1 2 3 5 8 in Java? ›**

In Java, a **Fibonacci series** is a sequence of numbers in which every third number equals the sum of the preceding two numbers. The fibonacci series' first two integers are 0 and 1. The Fibonacci Series Looks like this : 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89.............

**What is the missing number in the pattern 1 2 3 5 _ 13 21? ›**

1, 1, 2, 3, 5, 8, 13, 21, ... Solution: The Fibonacci series is the series of numbers 1, 1, 2, 3, 5, 8, 13, 21, ... Therefore, the next Fibonacci number in the following sequence is **34**.

**What is the 7th Fibonacci number the first Fibonacci numbers are 1 1 2 3 5 and 8? ›**

The notation that we will use to represent the Fibonacci sequence is as follows: f1=1,f2=1,f3=2,f4=3,**f5**=5,f6=8,f7=13,f8=21,f9=34,f10=55,f11=89,f12=144,…

### Is the Fibonacci sequence the series of numbers 0 1 2 3 5 8 13? ›

The Fibonacci sequence is the series of numbers: 0, 1, 1, 2, 3, 5, 8, 13, **21, 34**... In this series, the next number is found by adding the two numbers before it. Hence, the next term in the series is 8 + 13 = 21.

**Whose real name is the first few Fibonacci numbers 0 1 1 2 3 5 these numbers are named after Fibonacci? ›**

The man's full name was **Leonardo of Pisa**, or Leonardo Pisano in Italian.

**What are 5 Fibonacci sequences examples? ›**

Understanding the Fibonacci Sequence

For example, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377.

**What is the pattern rule of this sequence 1 3 5 7 9 11? ›**

The general term for the sequence 1, 3, 5, 7, 9, . . . is **2n - 1**.

**What is the rule for this sequence 1 2 1 3 1 4 1 5? ›**

The nth term of the sequence 1, 1/2, 1/3, 1/4, 1/5 is **1/n**.

**What is the 9th term of the sequence 1 1 2 3 5 8? ›**

9th Term in Sequence=**89**.

**What is the 9th term in the sequence 1 1 2 3 5 8 13? ›**

Fibonacci Numbers (Sequence):

1,1,2,3,5,8,13,**21,34,55,89,144,233,377**,...

**What is the pattern shown by the numbers 1 3 5 7 9 1 3 5 7 9? ›**

This is an arithmetic sequence since there is a common difference between each term. In this case, adding 2 to the previous term in the sequence gives the next term.

**What pattern is followed in the sequence 1 2 4 7 11 16 22 29? ›**

1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154, 172, 191, 211, ... Its three-dimensional analogue is known as the cake numbers. The difference between successive cake numbers gives the **lazy caterer's sequence**.

**What is the next term of the following sequence 1 2 3 4 5 8 7 16? ›**

Thus, the next term is **932**.

### What is the pattern rule for 0 1 3 6 10? ›

triangular numbers: 1, 3, 6, 10, 15, ... (these numbers can be represented as a triangle of dots). The term to term rule for the triangle numbers is to **add one more each time**: 1 + 2 = 3, 3 + 3 = 6, 6 + 4 = 10 etc. Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, ...

**What is the pattern for 2 2 6 6 8 8? ›**

**12,12** is the correct answer.

**How to print a pattern 1 12 123 1234 12345 in Java? ›**

**for(int i=1;i<=size;i++) // first loop which is used to print the series up to size.** **for(int j=1;j<=i;j++) // second loop which prints the one line elements**. 1 12 123 1234 12345. ( Here space means line change).

**What sequence is the sequence 1 2 1 4 1 6 1 8 an example of? ›**

This type of sequence is called a **geometric sequence**.

**What type of pattern is 1 2 3 4 5? ›**

This is an **arithmetic sequence** since there is a common difference between each term. In this case, adding 1 to the previous term in the sequence gives the next term.

**What is the next number in the following sequence 0 1 1 2 3 5 a 9 c 10 b 13 d 11? ›**

**0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,144,233,377,610,987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229**, ...

**What is the missing number in the series 1 2 3 5 11 7? ›**

Hence the missing number is **10**.

**What is the next number in the series 0 1 1 2 3 7? ›**

To find the next number in this series the same pattern is followed. 3 × 7 + 1 = 22 ; 7 × 22 + 1 = 155 ; and goes on. Hence the next number in this series is **0, 1, 1, 2, 3, 7, 22, 155**....

**What is the 7 term in the Fibonacci sequence? ›**

The 7th term of the Fibonacci sequence is **8**.

**What is the 12th Fibonacci number the first Fibonacci numbers are 1 1 2 3 5 and 8? ›**

The first 12 terms of the Fibonacci sequence are 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144. The 12th term (**144**) gives the number of rabbits after one year, which answers Fibonacci's original question to his readers.

### What are the first 7 odd numbers in the Fibonacci series? ›

Approach: Odd Fibonacci series is: **1, 1, 3, 5, 13, 21, 55, 89**...... Prefix sum of odd Fibonacci series is: 1, 2, 5, 10, 23, 44, 99, 188.....

**What is the 10th term of the sequence 1 1 2 3 5? ›**

tenth term in Fibonacci series is **55**.

**What is the 11th term of the Fibonacci sequence 1 1 2 3 5 8 13 21 34? ›**

The eleventh term of the sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, …... The 11th term will be **89**.

**How do you know if a sequence is in Fibonacci sequence? ›**

A number is Fibonacci **if and only if one or both of (5*n ^{2} + 4) or (5*n^{2} – 4) is a perfect square** (Source: Wiki).

**Did the golden ratio come from the Fibonacci sequence? ›**

The number 1.61803... is better known as the golden ratio, and frequently appears in art, architecture, and natural sciences. **It is derived from the Fibonacci series of numbers**, where each entry is recursively defined by the entries preceding it.

**Which came first Fibonacci or golden ratio? ›**

As has been pointed out by others, **the golden ratio is older than the Fibonacci numbers**.

**What made the Fibonacci sequence famous? ›**

Fibonacci is famous for **his contributions to number theory**. In his book, "Liber Abaci," he introduced the Hindu-Arabic place-valued decimal system and the use of Arabic numerals into Europe. He introduced the bar that is used for fractions today; previous to this, the numerator had quotations around it.

**What is the next number in the sequence 1 1 3 5 11 21? ›**

0, 1, 1, 3, 5, 11, 21, **43, 85, 171, 341, 683, 1365, 2731, 5461, 10923, 21845, 43691, 87381, 174763, 349525**, … (sequence A001045 in the OEIS) A Jacobsthal prime is a Jacobsthal number that is also prime.

**What is the rule of 2 5 8 11 14 17 20? ›**

This is an arithmetic sequence since there is a common difference between each term. In this case, **adding 3 to the previous term in the sequence gives the next term**.

**Is banana a Fibonacci sequence? ›**

Fruit: Bananas and apples **when cut in half, not lengthwise, show ridges that appear in the fibonacci sequence**, that is, 3 or 5, respectively. In flowers, plants, and trees, the pattern appears for several reasons, such as: To make use of the space for packaging and producing as many seeds as possible.

### Whose real name is the first Fibonacci numbers 0 1 1 2 3 5 8 13 these numbers are named after Fibonacci? ›

The man's full name was **Leonardo of Pisa**, or Leonardo Pisano in Italian.

**Which number does not belong in the following series 1 1 2 3 5 8 13? ›**

Answer: The number **4** does not belong to this series 1, 1, 2, 3, 4, 5, 8, 13, 21. Let us understand the rule of the series. Explanation: The given series is a Fibonacci Sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...

**What is the next term in the Fibonacci sequence 1 1 2 3 5 8? ›**

1, 1, 2, 3, 5, 8, 13, 21, ... Solution: The Fibonacci series is the series of numbers 1, 1, 2, 3, 5, 8, 13, 21, ... Therefore, the next Fibonacci number in the following sequence is **34**.

**What is the next term of the sequence 1 4 9 16 25 36 49? ›**

So, the next two terms in the sequence are **49, 64**.

**What is the 12th term of the Fibonacci sequence 1 1 2 3 5? ›**

The first 12 terms of the Fibonacci sequence are 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144. The 12th term (144) **gives the number of rabbits after one year**, which answers Fibonacci's original question to his readers.

**What is the rare Fibonacci sequence? ›**

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597… The last time we landed on a rare fibonacci sequence was **5-8-13**, and as you can see from the full sequence the previous occurrence was even further back. Mathematics can be found everywhere and Fibonacci numbers are especially prolific.

**Did Fibonacci find the golden ratio? ›**

Key Takeaways. The golden ratio is an irrational number that is equal to (1+√5)/2, or approximately 1.618... **The ratio is derived from an ancient Indian mathematical formula which Western society named for Leonardo Fibonacci, who introduced the concept to Europe.**

**What number is missing in the sequence 1 1 2 3 5 8 13 34? ›**

Hence, the correct answer is 21.

**What kind of sequence is this 1 2 3 5? ›**

**Fibonacci Numbers** (Sequence):

1,1,2,3,5,8,13,21,34,55,89,144,233,377,... Fn=Fn−2+Fn−1 where n≥2 . Each term of the sequence , after the first two, is the sum of the two previous terms.