Respuesta :
The given sequence 100,10,1,0.1, ........... does not form an AP as the common difference is not same.
What is the sequence of AP arithmetic progression?
In Arithmetic Progression, the difference between two mathematical orders is a fixed number (AP). Arithmetic Sequence is another name for it.
We'd come across a few key concepts in AP that had been labeled as:
- The first term (a)
- Common difference (d)
- Term nth (an)
- The total of first n terms (Sn)
As shown below, the AP can also be referred to in terms of common differences.
- The following is the procedure for evaluating an AP's n-th term: an = a + (n − 1) × d
- The arithmetic progression sum is as follows:Sn = n/2[2a + (n − 1) × d].
- Common difference 'd' of an AP: d = a2 - a1 = a3 - a2 = a4 - a3 = ...... = an - an-1.
Now, the stated sequence is; 100,10,1,0.1, ...........
The series comprises of four defined terms.
Consider the initial term be 'a₁' = 100.
Consider the second term be 'a₂' = 10.
Consider the third term be 'a₃' = 1.
And, consider the fourth term is 'a₄' = 0.1.
The AP must have the equal common difference. So,
d₁ = a₃ - a₂
Substitute the values.
d₁ = 1 - 10
d₁ = -9
Thus, the computed common difference is -9.
or d₂ = a₄ - a₃ (Substitute the values)
d₂ = 0.1 - 1
d₂ = -0.9.
As, for the result it is clear that the value of both common difference is not same. That is,
d₁ ≠ d₂.
Therefore, the given sequence doesn't not form an arithmetic sequence.
To know more about the arithmetic sequence, here
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