NCERT Class 10 Mathematics Chapter 5 Arithmetic Progressions

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

The general form of an AP is , , , ,..

2. A given list of numbers . . . is an AP, if the differences . . ., give the same value, i.e., if is the same for different values of k.

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

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

5. If l is the last term of the finite AP, say the nth term, then the sum of all terms of the AP is given by:

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