# Arithmetic Progressions Class 10 Notes Maths: Chapter 5

## Arithmeticprogressions

1. Sequence : A sequence is an arrangement of numbers or objects in a definite order.
2. A sequence a1, a2, a3, a4,…, an is called an Arithmetic Progression, if there exists a constant d such that a2 – a1 = d,
a3 – a2 = d,a4 – a3 = d,…, an+1 – an = d and so on. The constant d is called the common difference.
3. A sequence a1, a2, a3, a4,…, an is called an Arithmetic Progression, ifan+1 – an is independent of n.
4. sequence a1, a2, a3,..., an is an A.P., if and only if its nth term an is a linear expression in n and is such that the coefficient of n is the common difference.
5. The nth term an of an A.P. with the first term a and common difference d isgiven by an = a + (n – 1)d.
6. 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.
7. The sum of n terms of an A.P. with the first term a and common difference d is given by Sn = n/2{2a + (n – 1)d},or,
Sn = n/2{a + l}, where l = last term = a + (n – 1)d