Answer:
The formula to model the arithmetic sequence will be:
[tex]a_n=-0.3n+9[/tex]
Step-by-step explanation:
Given the sequence
[tex]8.7,\:8.4,\:8.1,\:7.8,\:7.5,...[/tex]
An arithmetic sequence has a constant difference d and is defined by:
[tex]\:a_n=a_1+\left(n-1\right)d[/tex]
Computing the differences between all adjacent terms:
[tex]8.4-8.7=-0.3,\:\quad \:8.1-8.4=-0.3,\:\quad \:7.8-8.1=-0.3,\:\quad \:7.5-7.8=-0.3[/tex]
The difference between all adjacent terms is the same and equal to
[tex]d=-0.3[/tex]
The first element of the sequence is
[tex]a_1=8.7[/tex]
so
[tex]a_n=a_1+\left(n-1\right)d[/tex]
Therefore, the nth term is computed by:
[tex]a_n=-0.3\left(n-1\right)+8.7[/tex] ∵ [tex]d=-0.3[/tex]
[tex]a_n=-0.3n+9[/tex]
Therefore, the formula to model the arithmetic sequence will be:
[tex]a_n=-0.3n+9[/tex]
