What is an Arithmetic Sequence?

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

Sequence

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,

What is Arithmetic Sequence?

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.

Example:
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.

Example: (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,…}

Rule

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

Example : 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 and a are:

  • 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

References

  1. https://pdfs.semanticscholar.org/a318/b30ce0239c43731610f354cdc7ad500eb77b.pdf
  2. https://www.sciencedirect.com/science/article/pii/S0096300308008837
  3. https://repository.unej.ac.id/handle/123456789/98520
AskAnyDifference HomeClick here
Search for "Ask Any Difference" on Google. Rate this post!
[Total: 0]
One request?

I’ve put so much effort writing this blog post to provide value to you. It’ll be very helpful for me, if you consider sharing it on social media or with your friends/family. SHARING IS ♥️

Subscribe
Notify of
guest
0 Comments
Inline Feedbacks
View all comments