**Arithmetic sequences and series**

A **Sequence **is the list of numbers written in a particular order following a pattern. A **Series** is the sum of the list of the numbers written in the specific order in a sequence. The sequence and series can have numbers extending up till infinity and they are called **infinite sequence and infinite series.**

**General Sequence:**

**Example:**

Write down the first few terms of the infinite sequence:

** {n+3 /n ^{2 }}^{∞}_{n=1}**

** n=1** means that the sequence is starting from 1^{st} number and going till infinity **->** the expression value by substituting n=1,2,3,…!

** When n=1, (n+3)/n ^{2 }=(1+3)/1^{2 }^{->} 4**

** When n=2, (n+3)/n ^{2} =(2+3)/2^{2 }**

^{->}

**5/4**

** When n=3, (n+3)/n ^{2} =(3+3)/3^{2 }**

^{->}

**6/9**

** So the sequence goes like**

** **

** {n+3 /n ^{2 }}^{∞}_{n=1 }={4,5/4,6/9,………..}**

** General Series:**

**Example:**

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