Respuesta :
Answer:
The sequence is + 1.25.
Step-by-step explanation:
The sequence is + 1.25
-1.75 + 1.25 = - 0.5
-0.5 + 1.25 = 0.75
0.75 + 1.25 = 2
2 + 1.25 = 3.25
From 2 to 3.25, you can clearly figure out the sequence by subtracting the two values.
The function that could be used to define and continue this function is f(n) = 1.25n -3
What is arithmetic sequence?
An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.
If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:
[tex]a, a + d, a + 2d, ... , a + (n+1)d, ...[/tex]
Its nth term is [tex]T_n = a + (n-1)d[/tex]
(for all positive integer values of n)
And thus, the common difference is
[tex]d = T_{n+1} - T_n[/tex]
for any positive integer values of n
For this case, the sequence is -1.75 -0.5 0.75 2 and 3.25
We can see that there is a constant difference between each conseqeuent terms as:
-0.5 - (-1.75) = 1.25
0.75 - (-0.5) = 1.25
2 - 0.75 = 1.25
3.25 - 2 = 1.25
So, there is a common difference between any two adjacent terms of this sequence.
That makes it an arithmetic sequence with:
- Initial term a = -1.75
- Difference = d =1.25
For nth term, this difference would've been added up (n-1) times (because of 2nd to nth terms each of them adding d to its previous term, which all started from 'a')
Thus, the nth term of this sequence is:
[tex]T_n = a + (n-1)d = -1.75 + (n-1)(1.25)\\\\T_n = 1.25n -3[/tex]
If we take [tex]T_n = f(n)[/tex] , then the function that gives the nth term is:
[tex]f(n) = 1.25n -3[/tex]
Thus, the function that could be used to define and continue this function is [tex]f(n) = 1.25n -3[/tex]
Learn more about arithmetic sequence here:
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