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 a₁, a₂, a₃, a₄,…, a_n is called an Arithmetic Progression, if there exists a constant d such that a₂ – a₁ = d,
a₃ – a₂ = d,a₄ – a₃ = d,…, a_n+1 – a_n = d and so on. The constant d is called the common difference.
A sequence a₁, a₂, a₃, a₄,…, an is called an Arithmetic Progression, ifan+1 – an is independent of n.
sequence a₁, a₂, a₃,..., 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