**Important Concepts and Formulas**

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

*a, a +d, a + 2d, a + 3d*, . . . where a is the first term of the AP and d is the common difference.
2. A given list of numbers

*a*. . . is an AP, if the difference_{1}, a_{2}, a_{3},*a*, . . ., give the same value, i.e., if_{2}– a_{1}, a_{3}– a_{2}, a_{4}– a_{3}*a*is the same for different values of k._{k + 1}– a_{k}
3. In an AP with first term

*a*and common difference*d*, the*n*th term (or the general term) is given by*a*_{n}= a + (n – 1)d.
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, or in an AP with n terms, if l is the nth term, then the sum of the n terms
of the AP is given by: