Sequences

Next, we will present some more complex sequences of numbers, including one of the most famous: the Fibonacci sequence.

The patterns of sequences vary from one to another.

Below, we present some examples of sequences with a different rule for each.

Note that the given rule can appear with: division, multiplication, addition, subtraction, or any combination of these.

If you are interested in this article, you may also be interested in the following articles:

• The real line
• Opposite numbers
• Integers
• Absolute value

You can find a variety of useful articles about mathematics in Tutorela !

$2, 4, 8, 16, 32$
In this sequence, to get from one term to the next we will multiply by $2$.

$2$

$4=2\times2$

$8=2\times4$

$16=2\times8$

And so on.

$3, 9, 27, 81, 243$
In this sequence, to get from one term to the next we need to multiply by $3$.
$3$

$9=3\times3$

$27=9\times3$

$81=27\times3$

$243=81\times3$

And so on.

$6, 4, 2, 0, -2$

In this sequence, to get from one term to the next we need to subtract $2$.

$6$

$4=6-2$

$2=4-2$

$0=2-2$

$-2=0-2$

$1000, 500, 250, 125, 62.5$
In this example, the operation used is division. In order to get from one term to the next, we divide the number by $2$.

$1000$

$500=1000:2$

$250=500:2$

$125=250:2$

$62.6=125:2$

$320, 80, 20, 5$

The rule of this sequence is to divide each number by $4$ to find the next number.

$320$

$80=320:4$

$20=80:4$

$5=20:4$

Try to work out the rule for each sequence:

• $1,3.75,6.5,9.25,12$
• $7,49,343,2401,16807$
• $0,-15,-30,-45,-60,-75$
• $891,297,99,33,11$
• $2,8,512,134217728$

Sequences are ordered sets of numbers that follow a rule or pattern.

A sequence is a set of ordered numbers. The numbers follow a rule that tells us how to obtain the numbers of the sequence using the previous ones. Many times the rules are governed by the operations of addition, subtraction, multiplication, division, or some combination thereof.

There are many types of sequences. For example, increasing and decreasing sequences, in which the numbers are either increasing or decreasing and following a certain pattern. There are also very famous sequences that have their own name, such as the Fibonacci sequence. In this series, the two previous numbers must be added to obtain the next number.