You pay $56 to rent a hotel room, but if you rent more than one room, you get a discount of $2 per room for each additional room rented.
(c) Say you rent n rooms. Find a formula showing how much each one costs as a function of n.R = (No Response) (d) Say you rent n rooms. Find a formula showing how much you will pay for all n rooms combined as a function of n.C = (No Response)
The first room costs 56, the second 56-2, the third 56-2-2. The general rule is simple:
k-th room costs 56-2*(k-1) which is equal to 58-2*k.
So if I understand correctly, the answer for (c) is 58-2*n.
Now let's sum these values for k=1..n:
Sum_k=1_k=n_[58-2*k] =Sum_k=1_k=n_ - 2*Sum_k=1_k=n_[k].
The first Sum is 58*n and the second is n*(n+1)/2 (the sum of the arithmetic progression).
So the result is 58*n - n*(n+1) which is equal to 57*n-n^2 or n*(57-n). It is the answer for the (d).
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