Arithmetic Progression(AP)

Finite AP

It is a sequence in which the di�erence between any two consecutive terms is constant.

1

An AP with countable number of terms. For e.g. 2, 4, 6, and 8.

In�nite APAn AP with uncountable number of terms. For e.g. 2, 4, 6, 8, 10, 12,...

nth Term Of an AP

For a set of positive numbers a1, a2, a3,...an , the arithmetic mean is

So, AM for two positive numbers

Where, tn = nth term a = 1st term d = common di�erence

Where, Sn = Sum of �rst n terms tn = nth term a = 1st term d = common di�erence

Sum Of �rst n Terms Of an AP

Consecutive Terms In AP

Arithmetic Mean

This constant di�erence is called as the common di�erence of the AP.2

tn = a + (n - 1)d

Sn = n_2

[ 2a + (n - 1)d ]

Sn = n_2

[ a + tn ]

AM = a1 + a2 + a3 +...+ an

n

AM =a + b

2

a - d , a , a + d3 terms1

a - 3d , a - d , a + d, a + 3d 4 terms2

a - 2d , a - d , a, a + d, a + 3d 5 terms3

Arithmetic Progression