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 a1,
a2, a3, . . . is an AP, if the difference a2
– a1, a3 – a2, a4 – a3,
. . ., give the same value, i.e., if ak + 1 – ak
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 an = 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:
