# Number Sequence

Integer Number Sequences

Integers are whole numbers. An integer number could be 0, 1, 2, etc. and these positive integer numbers are called natural numbers. Their counterparts are of course negative integers and are negative whole numbers, such as -3, -2 and -1. Integer sequences are therefore sequences based on whole numbers, both positive and negative and including zero, for instance:

-1, 1, 3, 5, 7, …

The number sequence can be specified explicitly by giving a formula for its nth term. The formula for this sequence is “2n−1″ for the nth term and can be called an explicit definition. Explicit meaning that you can chose any integer number for the letter “n” in the formula and it will generate a number in the sequence, for instance: n=3 will generate 2*3-1 = 5 as shown in the example.

An implicit number sequence is given by a relationship between its terms. For example, the Fibonacci sequence

0, 1, 1, 2, 3, 5, 8, 13, …

This number sequence is formed by starting with 0 and 1 and then adding any two consecutive terms to obtain the next one. This relationship is called an implicit description, since you cannot define this in such an easy formula with only one variable as in an explicit definition.

Rational Number Sequences

Unlike integers, rational numbers are numbers which can be written as a fraction where numerator and...

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