Question

Give an example of a sequence that is not an arithmetic sequence.

Answer 1

The sequence 2, 3, 5, 6..is example of the sequence which is not in arithmetic sequence AP.

What is the AP sequence (arithmetic progression)?

In Arithmetic Progression (AP), the distinction between two arithmetical orders is a constant. It is also known as Arithmetic Sequence.

Then we'd run into some important words in AP, such as:

• The first term (a)
• Common difference (d)
• Term nth (an)
• The total of first n terms (Sn)

The AP can also be described using common distinctions, as shown below.

• The following is the way to determine an AP's n-th term: an = a + (n − 1) × d
• The formula for arithmetic progression sum is as follows: Sn = n/2[2a + (n − 1) × d].
• Common difference 'd' is d = a2 - a1 = a3 - a2 = a4 - a3 = ......      = an - an-1.

Now, as per the question;

Consider any sequence. Let's say  2, 3, 5, 6..

Let's consider the first term is'a₁' = 2.

Let's consider 'a₂' = 3 is the second term.

Let's consider the third term is 'a₃' = 5.

Let's consider the fourth term be 'a₄' = 6

d₁  = a₂ - a₁      

Substitute the values;

d₁  = 3 - 2 = 1       ........(equation 1)

Now take the other set;

d₂  = a₃ - a₂    

d₂  = 5 - 3 = 2     .......(equation 2)

From the two equations 1 and 2. it is clear that the value of both common difference d₁ is not equal to d₂. Thus, the sequence considered is not in AP.

Therefore, the considered sequence 2, 3, 5, 6.. is not in AP.

To know more about the arithmetic progression, here

brainly.com/question/6561461

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