Searching for Patterns in Sequences: Arithmetic, Geometric and others

Meaning of Sequence:
Did you know that a sequence or progression is a set of numbers written in a special order by the application of a definite rule. Each number of the sequence is called a term. The first number is called the first term, followed by the second term, third term and so on.
Illustrative Examples:--------------Rule
A. 1,4,9,16,25.......................................Squaring counting numbers from 1 to 5
B. 2,4,6,8,10.........................................Every term after the first is obtained by adding 2
to the preceding one.