**What is Arithmetic Progression**

It is a series in which any two consecutive terms have a common difference and the next term can be

derived by adding that common difference to the previous term.

Therefore Tn+1 – Tn = constant and called common difference (d) for all n E N.

**Arithmetic ****Progression**

**Properties of an AP:**

I.** **If each term of an AP is increased, decreased, multiplied or divided by the same non-zero

number, the resulting sequence is also an AP.

** ***Example :*** **For A.P. 3, 5, 7, 9, 11…

II. In an AP, the sum of terms equidistant from the beginning and end is always same and

equal to the sum of first and last terms.

III.** **Three numbers in AP are taken as a - d, a, a + d.

For 4 numbers in AP are taken as a - 3d, a - d, a + d, a + 3d

For 5 numbers in AP are taken as a - 2d, a - d, a, a + d, a + 2d

IV.** **Three numbers a, b, c are in A.P. If 2b = a + c or b=(a+c)/2

and b is called the Arithmetic mean of a & c

**Formulae**

If a series is an A. P....

** a **= first term,

** d **= common difference = Tn - Tn-1

T(n) = nth term (Thus T1 = first term, T2 = second term, T10 tenth term and so on.)

** l **= last term,

** Sn **= Sum of n terms.

Let a, a + d, a + 2d, a + 3d,... are in A.P.

The nth* *term of an A.P is given by the formula **T(n) = a + (n - 1) d**

* Note :*** **If the last term of the A.P. consisting of n terms be l ,** l = a + (n - 1) d**

The sum of first n terms of an AP is usually denoted by Sn and is given by the following formula:

** Sn =n/2*[2a (n -1)d]=n/2(a+l)**

Where ‘*l’ *is the last term of the series.