# What is a Sequence?

A list of number in some particular order.

# Arithmetic Progression

An **arithmetic progression** is a sequence of numbers such that the difference of any two successive members is a constant

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**Features of Arithmetic Progression**

- The difference is called the
**common difference**of the AP and It is denoted by d - The members are called
**terms**. The first member is called first term - If a
_{1}, a_{2},a_{3},a_{4},a_{5}are the terms in AP then

d = a

_{2 }-a_{1}= a_{3}– a_{2. }= a_{4}– a_{3 }= a_{5}–a_{4} - We can represent the general form of AP in the form

a, a+d, a+2d, a+3d, a+4d ………..

Where

**a is first term**and**d is the common difference** - If the AP series has last term then it s finite Arithmetic Progression and if the AP series has infinite then it is called the infinite Arithmetic Progression

# nth Term of Arithmetic Progression

**Consider the following series: **a, a + d, a + 2d, a + 3d, …

a = First term a + d = Second term

a + 2d = Third term a + 3d = Fourth term and so on

## n

^{th}term = a + (n – 1)d

# Sum of n terms in Arithmetic Progression

## S = (n/2)[2a + (n – 1)d]

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