# NCERT Notes for Class 10 Maths Chapter 5 Arithmetic Progressions

#### Class 10 Maths Chapter 5 Arithmetic Progressions Notes

 Chapter Name Arithmetic Progressions Notes Class CBSE Class 10 Textbook Name NCERT Mathematics Class 10 Related Readings Notes for Class 10Notes for Class 10 MathsRevision Notes for Arithmetic Progressions

#### Sequence

A sequence is an arrangement of numbers in a definite order and according to some rule.
Example: 1, 3, 5,7,9, … is a sequence where each successive item is 2 greater than the preceding term and 1, 4, 9, 16, 25, … is a sequence where each term is the square of successive natural numbers.

#### Terms

The various numbers occurring in a sequence are called ‘terms’. Since the order of a sequence is fixed, therefore the terms are known by the position they occupy in the sequence.

Example: If the sequence is defined as

### Arithmetic Progression (A.P.)

An Arithmetic progression is a special case of a sequence, where the difference between a term and its preceding term is always constant, known as common difference, i.e., d. The arithmetic progression is abbreviated as A.P.

The general form of an A.P. is a, a + d, a + 2d,…

For example:

1, 9, 11, 13.., Here the common difference is 2. Hence it is an A.P.

In an A.P. with first term a and common difference d, the nth term (or the general term) is given
by .

an = a + (n – 1)d. …where [a = first term, d = common difference, n = term number

Example:

To find seventh term put n = 7

∴ a7 = a + (7 – 1)d or a7 = a + 6d

The sum of the first n terms of an A.P. is given by

where, 1 is the last term of the finite AP.

If a, b, c are in A.P. then  and b is called the arithmetic mean of a and c.