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Saturday, 25 February 2012

Progressions


A Progression is a sequence of numbers which have some kinf of relation. This relation determines what kind of a progression is. Generally, there are two types of progressions:
  1. Arithmetic Progression (AP)
  2. Geometric Progression (GP)
Any progression (AP or GP) can be generally expressed as
a_1 + a_2 + a_3 +\dots+ a_{n-1} + a_n
Total Terms: n
First Term: a_1
Last Term: a_n

Arithmetic Progression

In AP, the relation amoung sequence of numbers is that the difference between any two successive numbers is same.
Example: 3, 5, 7, 9, 11, 13, ... is an AP with difference 2. This difference is called common difference.
a_n = a_1 + (n - 1)d
S_n=\frac{n}{2}( a_1 + a_n)=\frac{n}{2}[ 2a_1 + (n-1)d]

Geometric Progression

In GP, each term after the first is found by multiplying the previous one by a fixed non-zero number called the common ratio. 
Example: 2, 6, 18, 54, ...
a + ar + ar^2 + ar^3 + ar^4 + \cdots


a_n = a\,r^{n-1}                                                                                                   NEXT

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