Sequences

A sequence is a set of numbers arranged one after another.

a1, a2, a3 ,..., an

3, 6, 9,..., 3n

The numbers a1, a2 , a3 , ..., are called terms or elements of the sequence.

The subscript is the set of positive integers 1, 2, 3, ... The subscript indicates the place that a term occupies in the sequence.

The nth term is denoted by an.

Calculation of a Sequence

By the Nth Term

an is a criterion that allows us to calculate any term of the sequence.

Example

an= 2n − 1

a1 = 2 ·1 − 1 = 1

a2 = 2 ·2 − 1 = 3

a3= 2 ·3 − 1 = 5

a4 = 2 ·4 − 1 = 7

1, 3, 5, 7, ..., 2n −1

Not all sequences have a general term. For example, the sequence of prime numbers:

2, 3, 5, 7, 11, 13, 17, 19, 23,...


By a Recursive Formula

A term is obtained by operating with the previous terms.

Example

Write a sequence whose first term is 2, knowing that each term is the square of the previous term.

2, 4, 16, ...

Fibonacci Sequence or Fibonacci Number

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, ...

The first two terms are one and the other terms are obtained by adding the two previous terms.