Examples of arithmetic sequences. Here it’s all about the arithmetic sequence. Have a look!

### Arithmetic sequence

Well, it’s an old topic from high school. So I’ll not go into much detail.

Suppose I have a sequence like .

Here is the first term and

Then this sequence is an arithmetic sequence.

There are also other sequences like geometric sequence, harmonic sequence and so on.

Now I’ll give some examples of arithmetic sequences.

#### Examples of arithmetic sequences

Here are some examples of arithmetic sequences.

Disclaimer: None of these examples is mine. I have chosen these from some book or books. The references are at the end of the post.

##### Example 1

According to Stroud and Booth (2013)* “The seventh and eleventh terms of an arithmetic sequence are

##### Solution

The standard form of an arithmetic sequence is

(1)

Here

Also, I already know the seventh and eleventh terms of the sequence as

So, first of all, I’ll put

But in the example, the seventh term is

(2)

Next, I’ll put

But in the example, the eleventh term is

(3)

Now I’ll solve equations (2) and (3) to get the values of

So, I’ll subtract equation (2) from equation (3).

Therefore I get

So it means

Now I’ll substitute this value of

Therefore I get

Next, I’ll simplify it to get the value of

Thus the value of

So I can conclude that the first term and the common difference are

This is the answer to this example.

Now I’ll go to my next example.

##### Example 2

According to Stroud and Booth (2013)* “If

##### Solution

First of all, I’ll choose the general term of the arithmetic sequence, say

Here

So let them be

So that means,

But from the example, I already know that the three successive terms are

(4)

(5)

(6)

Now my job is to find out the values of

###### Step 1

First of all, I’ll add equations (4), (5) and (6).

Therefore I get

This gives

But from equation (5), I already knpw that

So this means

Thus it gives

Therefore the three successive terms of the arithmetic sequence are

Thus I can say the first term

Hence I can say that the general form of this arithmetic sequence is

Now I already know the first three terms, that is

Next, I’ll find out the values of

Thus it will be

So the next four terms in this sequence are 39, 51, 63 and 75.

This is the answer to this example.

Now I’ll go to the next example.

##### Example 3

According to Stroud and Booth (2013)* “If

##### Solution

Here

(7)

Now I have to show that

So, first of all, I’ll simplify equation (7).

Thus it will be

So this means

Hence I have proved this statement.

This is the answer to this last example.

Dear friends, this is the end of today’s post. Thank you very much for reading this. Please let me know how you feel about it. Soon I will be back again with a new post. Till then, bye, bye!!

## Leave a Reply