The expression
can be used to describe the sequence 0,1,2,3,... where n will represent the position of a term in the sequence where n = 1 is for the first term.
The given sequence is 0, 1, 2, 3, .......
We will use n to represent the position of a term such that n = 1 for the first term, n = 2 for the second term, n= 3 for the third term, and n = 3 for the third term in the given sequence.
What is an arithmetic sequence?
It is a sequence of numbers where the difference between the consecutive terms is same.
The nth term in an arithmetic sequence is given by:
.
The given sequence 0, 1, 2, 3, ...... is an arithmetic sequence.
d = 1 - 0 = 1
d = 2 - 1 = 1
d = 3 - 2 = 1
The difference between the consecutive terms is the same.
In the sequence 0, 1, 2, 3, ......
![a_1 = 0, a_2=1, a_2=2, a_3=3, and~so~on.](https://tex.z-dn.net/?f=a_1%20%3D%200%2C%20a_2%3D1%2C%20a_2%3D2%2C%20a_3%3D3%2C%20and~so~on.)
If we use the arithmetic sequence nth term formula
we get,
![a_1=0+(1-1)1=0\\a_2=0+(2-1)1=1\\a_3=0+(3-1)1=2\\a_4=0+(4-1)1=3\\...\\...\\...](https://tex.z-dn.net/?f=a_1%3D0%2B%281-1%291%3D0%5C%5Ca_2%3D0%2B%282-1%291%3D1%5C%5Ca_3%3D0%2B%283-1%291%3D2%5C%5Ca_4%3D0%2B%284-1%291%3D3%5C%5C...%5C%5C...%5C%5C...)
Thus the expression
can be used to describe the sequence 0,1,2,3,... where n will represent the position of a term in the sequence where n = 1 is for the first term.
Or we can simply say
since
.
Learn more about arithmetic sequence here:
brainly.com/question/16415816
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