idunno456
13.06.2020 •
Mathematics
⎧
f(1)=−8
f(n)=f(n−1)−3
Find an explicit formula for f(n)f(n)f, left parenthesis, n, right parenthesis
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Ответ:
f(n)=-5-3n
Step-by-step explanation:
Given the recursive formula of a sequence
f(1)=−8
f(n)=f(n−1)−3
We are to determine an explicit formula for the sequence.
f(2)=f(2-1)-3
=f(1)-3
=-8-3
f(2)=-11
f(3)=f(3-1)-3
=f(2)-3
=-11-3
f(3)=-14
We write the first few terms of the sequence.
-8, -11, -14, ...
This is an arithmetic sequence where the:
First term, a= -8
Common difference, d=-11-(-8)=-11+8
d=-3
The nth term of an arithmetic sequence is determined using the formula:
T(n)=a+(n-1)d
Substituting the derived values, we have:
T(n)=-8-3(n-1)
=-8-3n+3
T(n)=-5-3n
Therefore, the explicit formula for f(n) can be written as:
f(n)=-5-3n
Ответ:
5th grade mean: 4.67
7th grade mean: 3.46
5th grade median: 5
7th grade median: 3.5
Step-by-step explanation:
I did the math :) (also sorry if this is late, I was looking for the answer but no one had it, so I decided to help out other peeps with the same problem)