Respuesta :
Answer:
[tex]a_n = -2 + n[/tex] is an expression which describe the given sequence
Step-by-step explanation:
Arithmetic sequence states that a sequence where the difference between each successive pair of terms is the same.
The general rule for the arithmetic sequence is given by;
[tex]a_n =a_1+(n-1)d[/tex] ......[1]
where
[tex]a_1[/tex] represents the first term
d represents the common difference
and n is the number of terms;
Given sequence: -1 , 0 , 1 , 2 , .....
This is an arithmetic sequence with common difference
Since,
0-(-1) = 1
1-0 =1
2-1 = 1 ....
Here, [tex]a_1 = -1[/tex]
Substitute the value of [tex]a_1 = -1[/tex] , d =1 in [1] we get
[tex]a_n = -1 +(n-1)(1)[/tex]
[tex]a_n = -1 + n -1 = -2 +n[/tex]
Therefore,an expression which describe the given sequence is, [tex]a_n = -2 + n[/tex]
An expression which describe the given sequence is, [tex]a_n=-2+n[/tex]
[tex]a_n=-2+n[/tex] is an expression which describe the given sequence
Arithmetic sequence states that a sequence where the difference between each successive pair of terms is the same.
What is the general formula for arithmetic sequence?
The general rule for the arithmetic sequence is given by,
[tex]a_n=a+(n-1)d[/tex] ......[1]
where,[tex]a_1[/tex] represents the first term
d = common difference
n = number of terms;
Given sequence is -1 , 0 , 1 , 2 , .....
This is an arithmetic sequence with common difference
Since,0-(-1) = 1
1-0 =1
2-1 = 1 ....
Here, [tex]a_1=-1[/tex]
Substitute the value of [tex]a_1=-1[/tex] , d =1 in [1] we get,
[tex]a_n=-1+(n-1)(1)[/tex]
[tex]a_n=-2+n[/tex]
Therefore,an expression which describe the given sequence is, [tex]a_n=-2+n[/tex]
To learn more about the arithmetic sequence visit:
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