Maths Class 10 Chapter 5: Arithmetic Progression

# Maths Class 10 Chapter 5: Arithmetic Progression

Important Concepts and Formulas

1.      An arithmetic progression (AP) is a list of numbers in which each term is obtained by adding a fixed number d to the preceding term, except the first term. The fixed number d is called the common difference.
The general form of an AP is a, a +d, a + 2d, a + 3d, . . . where a is the first term of the AP and d is the common difference.

2.      A given list of numbers a1, a2, a3, . . . is an AP, if the difference a2 – a1, a3 – a2, a4 – a3, . . ., give the same value, i.e., if ak + 1 – ak is the same for different values of k.

3.      In an AP with first term a and common difference d, the nth term (or the general term) is given by       an = a + (n – 1)d.

4.      The sum of the first n terms of an AP is given by:

5.      If l is the last term of the finite AP, or in an AP with n terms, if l is the nth term, then the sum of the n terms of the AP is given by: