Answer:
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
Answer: (y - 2) (y -3)
Step-by-step explanation:
One weights 30lbs the other weights 54lbs
Answer:
Graph of the inequality 3y-2x>-18 is given below.
Step-by-step explanation:
We are given the inequality, 3y-2x>-18
Now, using the 'Zero Test', which states that,
After substituting the point (0,0) in the inequality, if the result is true, then the solution region is towards the origin. If the result is false, then the solution region is away from the origin'.
So, after substituting (0,0) in 3y-2x>-18, we get,
3\times 0-2\times 0>-18
i.e. 0 > -18, which is true.
Thus, the solution region is towards the origin.
Hence, the graph of the inequality 3y-2x>-18 is given below.