CBSE Class 10 Maths Notes Chapter 5 Arithmetic Progressions Pdf free download is part of Class 10 Maths Notes for Quick Revision. Here we have given NCERT Class 10 Maths Notes Chapter 5 Arithmetic Progressions.
CBSE Class 10 Maths Notes Chapter 5 Arithmetic Progressions
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.
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
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
Sn = [2a + (n – 1)d] or [a + 1]
where, 1 is the last term of the finite AP.
If a, b, c are in A.P. then b = and b is called the arithmetic mean of a and c.
Class 10 Maths Notes
- Chapter 1 Real Numbers Class 10 Notes
- Chapter 2 Polynomials Class 10 Notes
- Chapter 3 Pair of Linear equations in Two Variables Class 10 Notes
- Chapter 4 Quadratic Equations Class 10 Notes
- Chapter 5 Arithmetic Progressions Class 10 Notes
- Chapter 6 Triangles Class 10 Notes
- Chapter 7 Coordinate Geometry Class 10 Notes
- Chapter 8 Introduction to Trigonometry Class 10 Notes
- Chapter 9 Some Applications of Trigonometry Class 10 Notes
- Chapter 10 Circles Class 10 Notes
- Chapter 11 Constructions Class 10 Notes
- Chapter 12 Areas related to Circles Class 10 Notes
- Chapter 13 Surface Areas and Volumes Class 10 Notes
- Chapter 14 Statistics Class 10 Notes
- Chapter 15 Probability Class 10 Notes