What is Sequence

Introduction for Sequences

A set of numbers arranged in a definite order according to some definite rule is called a sequence.

A sequence is a function whose domain is the set N of natural numbers.

It is customary to denote a sequence by a letter 'a' and the image a(n) or t(n), n Î N under 'a' by a_n or t_n.

Sequences have wide applications. For example, the amount of money in a fixed deposit in a bank, over a number of years increases in a sequence.

OR

Sequence means a succession of numbers whose order is determined by a rule or a function. So it is an ordered set of numbers a₁, a₂, ---------a_n. Here a₁, a₂ etc are called terms.

If the numbers of the terms in a sequence is unlimited it is called an infinite sequence and the general term of a sequence is denoted by an. A sequence can be considered a function whose domain is set of integers.

F (n) =a_n where n = 1, 2, 3 etc.

Sequence general term a_n
½, 2/3, 3/4, 4/5 n/(n+1)
½, ¼, 1/8 1/2ⁿ
1/2, -2/3, ¾ (-1) ⁿ⁺¹ n/(n+1)
1, 3, 5, 7 (2n-1)