# What is an Arithmetic Sequence?

For understanding the term ‘Arithmetic Sequence’, first we have to understand what is the meaning if sequence.

## Urutan

A sequence is a group of numbers, which are in order. For example; 3,5,7,9… and so on.

Each number in the sequence or group of numbers is called a term. Sometimes they are called “elements” or “members”. Now,

## Apa itu Urutan Aritmatika?

In this sequence, the difference between one term and the next follows a constant behaviour. In other words, in here we add the same value or term each time to the infinity.

Contoh:
1,4,7,13,16,19,20,25,… here, this sequence follows the difference of 3 between numbers. The pattern is continuous by adding three each time as shown below,

So, commonly we write a correct sequence like this, or the formula for the correct sequence is;

{a, a+d, a+2d, a+3d, …}

In here,

• ‘a’ represents the first term of the sequence, and
• ‘d’ represents the difference between the terms, which is called the (common difference) of the sequence.

Contoh: (Continued from above)

1,4,7,13,16,19,20,25,…

It has,

• ‘a’ = 1 (which is the 1st term)
• ‘d’ = 3 (which is the “common difference” between the terms)

We get,

Formula is : { a, a+d, a+2d, a+3d,…}
{ 1, 1+3, 1+2×3, 1+3×3,…}
{1,4,7,10,…}

## Aturan

We can also write ‘AS’ (Arithmetic Sequence) as a rule,

Xn = a + d(n-1)
We use “n-1” because in the first term the ‘d’ is not used

Contoh : Find the 9th term from this sequence.

3, 8, 13, 18, 23, 28, 33, 38, …

Now, this sequence here has a common difference of 5 between them.

The value of D dan Sebuah adalah:

• d = 5 (the common difference between the terms)
• a = 3 (the first term of the sequence)

Now, by using the formula,

Xn = a + d(n-1)
= 3 + 5(n-1)
= 3 + 5n – 5
= 5n – 2

hence, the 9th term is. Here, n = 9.

X9 = 5 x 9 – 2
= 43

Daftar Isi

x
2D vs 3D