## Arithmetic Sequence

 First Number Common Difference nth Number to obtain

## Geometric Sequence

 First Number Common Ratio nth Number to obtain

## Fibonacci Series

Nth number to obtain

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= 16

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# How sequences are made?

### A brief introduction

In number system a sequence is a set of numbers (with repetition allowed) that follows a particular pattern.

Example:

Sequence 1: 1, 4, 7, 10, 13, ?, ?

Answer 15 and 18 respectively

Explanation: difference between numbers is 3

Sequence 2: 2, 4, 8, 16, 32, ?, ?

Answer 64 and 128 respectively

Explanation: next number is multiplied by 2 of the previous number

There are different types of sequences

1.Arithmetic sequence
2.Geometric sequence
3.Fibonacci sequence

### Formula for calculating arithmetic sequence

first number = a;
common difference = d;
nth number = n

nth number = a + (n-1) * d

Example:

first number = 5
common differnece = 5
n = 4
4th number = 5 + (4-1) * 5
4th numnber = 20

### Formula for calculating geometric sequence

first number = a;
common ratio = r;
nth number = n

nth number = a * ((1-r n )/(1-r))

Example:

first number = 2
common differnece = 3
n = 4
nth number = 2 * ((1-3 4 )/(1-3))

nth numnber = 80

### Fibonacci sequence

Fibonacci is a sequence of numbers whose next number is equal to sum of previous two numbers.

Example:

Fibonacci numbers of length 9
1, 1, 2, 3, 5, 8, 13, 21, 34,.......

### Some interesting facts about Sequences

An famous astronomer named Halley in the year 1606 found an unusual phenomenon in the night sky. He found a glowing object passing through the sky leaving behind a trail of dust and ice, which is called a comet. He recalled his memory that the same phenomenon was happened in the 1530. By observing these values he predicted the next few years of the arrival of that comet. This comet is called as Haleys comet and the next appearance of the comet is 2062.

This is a real world example of arithmetic sequence where

first number = 1530
Common difference = 76
Sequence predicted: 1530, 1606, 1682, 1758, 1834, 1910, 1986, 2062, 2138