Arithmetic sequence

This post will give you information on Arithmetic sequence, Below i have the definition and an example for it.

Definition of Arithmetic sequence:- A sequence in which each term, except the first is obtained by adding a fixed number to the term immediately preceding it is called "Arithmetic Sequence". This fixed number is the difference of two successive terms and is called as "Common Difference" usually denoted by the letter 'd'. Quantities are said to be in Arithmetic Sequence when they increase or decrease by a common difference.

Below are the examples for arithmetic sequence, just look at them carefully.

1) The sequence 1,3,5,7,9,. . . . . .is an arithmetic sequence since the difference between two consecutive terms is always 2.

2) The sequence -1,-4,-7,-10,. . . . .is an arithmetic sequence since the difference between two consecutive terms is always -3.

I have another simple example, look at the numbers below

4, 8, 12, 16, 20......

This arithmetic sequence has a common difference of 4 in them. Therefore we add 4 to get the next term of the sequence.

They are two ways of writing the n^th term of an arithmetic sequence

1) Recursive Formula

a_n=a+ (n-1) d

Recursive formula becomes difficult if we want to find 50^th term because we need to find first 49 terms in order to find 50^th term.

2) Explicit Formula

Explicit formula is also called as closed form.

Interesting right? We will discuss on how to solve arithmetic sequence in my next post. Well i am going to write more let me know your comments on this.