Geometric Progression

A geometric progression (also known as a geometric sequence or a geometric series) is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed number called the common ratio. Example: 1,3,9,27... common ratio is 3.

Also a, b, c, d, ... are said to be in Geometric Progression (GP) if b/a = c/b = d/c etc.

1.A GP is of the form etc. Where a is the first term and r is the common ratio.

2.The nth term of a Geometric Progression is given by
.

3.The sum of the first n terms of a Geometric Progression is given by

1.When r<1 or r>1

2.When r =1 the progression is constant of the for a,a,a,a,a,...etc.

4.Sum of the infinite series of a Geometric Progression when |r|<1 is:

5.Geometric Mean (GM) of two numbers a and b is given by .