These comprehensive RBSE Class 10 Maths Notes Chapter 5 Arithmetic Progressions will give a brief overview of all the concepts.

## RBSE Class 10 Maths Chapter 5 Notes Arithmetic Progressions

1. An arithmetic progression (AP) is a list of numbers in which each term is obtained by adding a fixed number to the preceding term (except the first term). This fixed number d is called the common difference of the arithmetic progression, d can be positive, negative or zero.

2. a, a + d, a + 2d, a + 3d,.. represents an arithmetic progression, where a is the first term and d the common difference. This is called the general form of an A.P.

3. A given list of numbers a_{1}, a_{2}, a_{3 ………… }is an A.P., if the differences a_{2} – a_{1} a_{3} – a_{2}, a_{4} – a_{3} give the same value, i.e., if a_{k+x} – a_{k} is the same for different values of k.

4. The n^{th} term (or the general term) an of the AP with first term a and common difference d is determined by the following formula

[ a_{h} = a + (n- 1 )d, where n is a natural number.

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

S = \(\frac{n}{2}(a + l)\) [2a+ (n- 1 )d] where n is a natural number.

6. If / is the last term of a finite A .P. (say the n^{th} term), then the sum of all the terms of the AP is given by

S =\(\frac{n}{2}(a + l)\)(a+1)

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

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