First Number 

Common Difference 

nth Number to obtain 
First Number 

Common Ratio 

nth Number to obtain 
Nth number to obtain
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Numbers are said to be in sequence if they follow a particular pattern or order. Let us discuss three types of sequences in this post: Arithmetic, Geometric and Fibonacci.
The terms a1, a2, a3, a4, a5, ……an are said to be in an arithmetic progression P, when a2a1=a3a2, i.e. when the terms increase or decrease continuously by a common value. This common value is called the common difference (d) of the Arithmetic Sequence.
The first term of the P is denoted as ‘a’ and the number of terms is denoted as ‘n’. We also call an arithmetic sequence as an arithmetic progression.
Common Difference is the difference between the successive term and its preceding term. It is always constant for the arithmetic sequence.
Common difference (d) = a2 – a1
To find the nth term of an arithmetic sequence, we use
Sum of terms of an Arithmetic sequence is

= 

Where ‘a’ is the first term and ‘d’ is the common difference.
Examples of Arithmetic Progression:
1. 5, 7, 9, 11, 13, ...Here ‘5’ is the first term and the common difference d = 75 = 2
2. 15, 12, 9, 6, 3, 0, 3, 6 ,…Here ‘15’ is the first term and the common difference d = 1215 = 3
The terms a1, a2, a3, a4, a5……an are said to be in geometric sequence, when a2/a1=a3/a2=r, where ‘r’ is called the common ratio(r) of the Geometric Sequence.
The first term of the sequence is denoted as ‘a’ and the number of terms is denoted as ‘n’. We also call a geometric sequence as a geometric progression.
Common Ratio is the ratio between the successive term and its preceding term. It is always constant for a given geometric sequence.

= 

To find the nth term of a geometric sequence, we use
Sum of terms of a geometric sequence is

= 

where ‘a’ is the first term and ‘r’ is the common ratio.
Sum of terms of an infinitely long decreasing geometric sequence is

= 

Examples of Geometric Progression:
1. 1, 2, 4, 8, 16….
Here ‘1’ is the first term and the common ratio(r) = 2/1 = 2
2. 1, 2, 4, 8, 16…
Here ‘1’ is the first term and the common ratio(r) = 2/(1) = 2
The Fibonacci Sequence is the series of numbers  0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...
The next number of the series is obtained by adding up the two numbers before it.
You can use our series calculator for calculating and finding out any numbers from arithmetic, geometric and Fibonacci series.
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