# Leaving Certificate Mathematics/Sequences and Series

**Introduction**

You are very familiar with sequences, if indeed you do not think you are. but let us show you that.

### Example

The natural numbers, 1, 2, 3 etc that you are familiar with form a sequence, right?. That is, in order to obtain the next digit, we just add one, right?. This is known as an **arithmetical sequence**, because to use the technical jargon, it uses the arithmetical operation of **addition** to determine the next digit in the sequence. i.e. you add one each time to get the next digit.

At the Leaving Cert Ordinary Level there are two basic sequences that are studied, arithmetic sequences and non-linear sequences.And we will explain both.

### Arithmetic sequences (progressions)

Like all arithmetic sequences (sometimes called "arithmetic progressions"), the sequence continues, one digit after another, in a constant pattern, by the addition of a constant number which is added on to the previous number.

### Example

Q. A certain arithmetic sequence begins 2, 4, 6, 8.. what is the next number?

Did you guess 10? because the difference between the "terms"(as the digits are called) of this sequence is 2.i.e

2+2=4

4+2=6

6+2=8

8+?=

hat we want to express is as follow that the arithmetic sequence is: 2(+2), 4(+2), 6(+2),8(+2). This is the reason it is called an arithmetic sequence. When we look at other sequences we will see that they don't involve the arithmetic operation of addition, and so are not classified as arithmetic sequences (or progressions).