# Arithmetic Progressions Class 10 Notes Maths: Chapter 5

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## Arithmetic progressions

**Sequence :**A sequence is an arrangement of numbers or objects in a definite order.- A sequence a
_{1}, a_{2}, a_{3}, a_{4},…, a_{n}is called an Arithmetic Progression, if there exists a constant d such that a_{2}– a_{1}= d,

a_{3}– a_{2}= d,a_{4}– a_{3}= d,…, a_{n+1}– a_{n}= d and so on. The constant d is called the common difference. - A sequence a
_{1}, a_{2}, a_{3}, a_{4},…, an is called an Arithmetic Progression, ifan+1 – an is independent of n. - sequence a
_{1}, a_{2}, a_{3},..., an is an A.P., if and only if its nth term a_{n}is a linear expression in n and is such that the coefficient of n is the common difference. - The n
^{th}term an of an A.P. with the first term a and common difference d isgiven by a_{n}= a + (n – 1)d. - If there are m terms of an A.P. with the first term as a and the common difference as d then, nth term from the end

= (m – n + 1)^{th}term from the beginning = a + (m – n) d.Also, nth term from the end = l – (n – 1)d, where l denotes the last term. - The sum of n terms of an A.P. with the first term a and common difference d is given by S
_{n}= n/2{2a + (n – 1)d},or,

S_{n}= n/2{a + l}, where l = last term = a + (n – 1)d