Respuesta :
Answer:
[tex]a_n = 14-1.5n[/tex]
Step-by-step explanation:
The explicit rule for the arithmetic sequence is given by:
[tex]a_n =a_1+(n-1)d[/tex] ....[1]
where,
[tex]a_1[/tex] is the first term
d is the common difference and n is the number of terms.
Given sequence:
12.5, 11, 9.5, 8, 6.5, 5 ...
This is an arithmetic sequence.
here, [tex]a_1=12.5[/tex] and d =- 1.5
Substitute these in [1] we have;
[tex]a_n = 12.5+(n-1)(-1.5)[/tex]
⇒[tex]a_n = 12.5-1.5n+1.5[/tex]
⇒[tex]a_n = 14-1.5n[/tex]
Therefore, the explicit rule for the given sequence is, [tex]a_n = 14-1.5n[/tex]
The explicit rule for the given sequence is [tex]\rm a_n =14-1.5n[/tex].
It is given that the sequence 12.5, 11, 9.5, 8, 6.5, 5 ...
It is required to find the explicit rule for the sequence.
What is a sequence?
It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
We have an arithmetic sequence:
12.5, 11, 9.5, 8, 6.5, 5 ...
The explicit rule for the above sequence can be given by:
[tex]\rm a_n=a_1+(n-1)d[/tex] .....(1)
Where [tex]\rm a_1=12.5[/tex] and
[tex]\rm d= 11.5-12\Rightarrow-1.5[/tex]
Putting these values in the equation (1), we get:
[tex]\rm a_n=12.5+(n-1)\times(-1.5)[/tex]
[tex]\rm a_n = 12.5-1.5n+1.5\\\\\rm a_n =14-1.5n[/tex]
Thus, the explicit rule for the given sequence is [tex]\rm a_n =14-1.5n[/tex].
Learn more about the sequence here:
brainly.com/question/21961097
