### Class 10 Math,Chapter 5 Arithmetic Progression

**Class X Math**

Notes for Arithmetic Progression

Notes for Arithmetic Progression

A group of numbers connected by a definite law is known as sequence.

**Arithmetic Progression**

A Sequence in which each term is obtained from the preceeding term by adding a constant quantity to it.

A sequence is called a series if its terms are connected by the sign of addition or subtraction.

*n*th term of an Arithmetic Progression

*an*=

*a*+ (

*n*- 1)

*d*=

*l*

where

*a*is first term**,***d*is common difference*and l*is last term.**Selection of terms of an A.P.**

**•**When odd number of terms are required. Take middle term as ‘

*a*’ and common difference as ‘

*d*’.

**•**When even number of terms are required take

*a*-

*d*,

*a*+

*d*as two middle terms and ‘2

*d*’ as common difference.

The condition for three terms to be in an Arithmetic Progression is that common difference between them must be same.

⇒

*t*‐_{3}*t*=_{2}*t*–_{2}*t*_{1}
Sum of n terms of an A.P.

*l*is the last term

*a*is the first term

*d*is the common difference

*n*th term from the end is

*l*- (

*n*- 1)

*d*.

where

*l*is last term,*d*is common difference.
The Standard form of an Arithmetic Progression is

*a*+ (

*a*+

*d*) + (

*a*+ 2

*d*) + .... (

*l*-

*d*) +

*l*

*a*is first term,

*l*is last term,

*d*is common difference

*n*th term of an Arithmetic Progression is the difference of the sum to first

*n*terms and the sum to first (

*n*- 1) terms

*an*=

*Sn*-

*Sn*- 1

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