Answer:
[tex]\begin{aligned}\bullet\ &f(1)=800;f(n)=f(n-1)+900, \text{for $n\ge 2$}\\ \bullet\ & f(n)=900n-100\end{aligned}[/tex]
Step-by-step explanation:
The total mileage by month is an arithmetic sequence with a first term of 800 and a common difference of 900. Using the general form for such a sequence, ...
an = a1 +d(n -1)
an = 800 +900(n -1) = 900n -100
Then, as a function of n, this can be written ...
f(n) = 900n -100
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When considered as a recursive relation, we find the first term is still 800:
f(1) = 800
and that each term is 900 more than the previous one:
f(n) = f(n-1) +900 . . . . for n ≥ 2
You have to consider that many of the various answer choices are corruptions of one or the other of these forms, so you must examine them carefully.
