The sequence 2, 3, 5, 6..is example of the sequence which is not in arithmetic sequence AP.
<h3>What is the AP sequence (arithmetic progression)?</h3>
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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