Sequences

Sequences

In the previous lesson, we learned about pattern of numbers. In this lesson we discuss about Sequences.

A sequence is an ordered list of numbers.

The sum of the terms of a sequence is called a series.

  • Each number of a sequence is called a term (or element) of the sequence.
  • A finite sequence contains a finite number of terms (you can count them). 1, 4, 7, 10, 13
  • An infinite sequence contains an infinite number of terms (you cannot count them). 1, 4, 7, 10, 13, . . .
  • The terms of a sequence are referred to in the subscripted form shown below, where the natural number subscript refers to the location (position) of the term in the sequence.Sequences 1

(If you study computer programming languages such as C, C++, and Java,
you will find that the first position in their arrays (sequences) start with a subscript of zero.)

The general form of a sequence is represented:

  • The domain of a sequence consists of the counting numbers 1, 2, 3, 4, … and the range consists of the terms of the sequence.
  • The terms in a sequence may, or may not, have a pattern, or a related formula.
  • For some sequences, the terms are simply random.

Let’s examine some sequences that have patterns:

Sequences often possess a definite pattern that is used to arrive at the sequence’s terms.

It is often possible to express such patterns as a formula. In the sequence shown at the left, an explicit formula may be:

Sequences 2

Examples:

Sequences 3

Sequences 4

Sequences 5

Sequences 6

Maths