Arithmetic Progressions Class 10 Notes Maths Chapter 5

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. According to new CBSE Exam Pattern, MCQ Questions for Class 10 Maths Carries 20 Marks.

CBSE Class 10 Maths Notes Chapter 5 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 .
a_n = 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
S_n = \(\frac { n }{ 2 }\)[2a + (n – 1)d] or \(\frac { n }{ 2 }\)[a + 1]
where, 1 is the last term of the finite AP.

If a, b, c are in A.P. then b = \(\frac { a+c }{ 2 }\) and b is called the arithmetic mean of a and c.

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