The expression [tex]a_n = a_1 + (n-1)d[/tex] 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:
[tex]a_n = a_1 + (n-1)d\\where~a_1=first~term~and ~d=common~difference[/tex].
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, ......
[tex]a_1 = 0, a_2=1, a_2=2, a_3=3, and~so~on.[/tex]
If we use the arithmetic sequence nth term formula
we get,
[tex]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\\...\\...\\...[/tex]
Thus the expression [tex]a_n = a_1 + (n-1)d[/tex] 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 [tex]a_n=n-1[/tex] since [tex]a_1=0 ~and~ d=1[/tex].
Learn more about arithmetic sequence here:
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