SOLUTION: The recursive rule for a sequence is f(1)=8 1/2, f(n)=f(n-1)-1/2. How should I find the explicit rule?

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Question 1102910: The recursive rule for a sequence is f(1)=8 1/2, f(n)=f(n-1)-1/2.
How should I find the explicit rule?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
f%28n%29=f%28n-1%29-1%2F2

f%28n%29-f%28n-1%29+=+-1%2F2

The left side is the difference between one term
and the preceding term.

So this is an arithmetic sequence with
common difference = d=-1%2F2 and first term a%5B1%5D=f%5B1%5D=8%261%2F2

a%5Bn%5D=a%5B1%5D%2B%28n-1%29d

f%5Bn%5D=8%261%2F2%2B%28n-1%29%28-1%2F2%29

f%5Bn%5D=17%2F2-expr%281%2F2%29%28n-1%29

f%5Bn%5D=17%2F2-expr%281%2F2%29n%2B1%2F2

f%5Bn%5D=18%2F2-expr%281%2F2%29n

f%5Bn%5D=9-expr%281%2F2%29n   <-- explicit rule

Edwin