ABSTRACT
A sequence of numbers is a set of numbers which follow a pattern or rule. Any number in a sequence can be predicted from the previous one once the rule has been determined. Each number in a sequence is called a term. When the terms of a sequence are linked together algebraically it is called a series. A series can be finite or infinite depending upon whether it terminates after a definite number of terms or not. A series of numbers is said to be in arithmetic progression if the difference between consecutive terms is constant. This difference is called the common difference. A series of numbers is said to be in geometrical progression if the ratio of each term of the series to its preceding term is a constant value. This ratio is known as the common ratio. Binomial expansions are useful for numerical approximations, for calculations with small variations and errors and also in probability theory.
