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 a1, a2, a3 ………… is an A.P., if the differences a2 – a1 a3 – a2, a4 – a3 give the same value, i.e., if ak+x – ak is the same for different values of k.
4. The nth term (or the general term) an of the AP with first term a and common difference d is determined by the following formula
[ ah = 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 nth 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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