How are x, y, and z related in their sequences?

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The discussion focuses on the relationships between the sequences of x, y, and z, with specific formulas provided for each. The nth term for x is expressed as 3n, for y as 30-2n, and for z as 11-0.5n. A formula for z in terms of x and y is derived, showing multiple valid solutions, including z(x,y) = y/4 + 7/2. The original book's answer for z is given as z = (1/2)(52-x-y). Overall, the thread emphasizes the interconnectedness of the sequences and the flexibility in deriving formulas.
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The lists below show the relationship between value of x, y & z.
List A, x: 3, 6, 9, 12, 15,...
List B, y: 28, 26, 24, 22, 20,...
List C, z: 10.5, 10, 9.5, 9, 8.5,...
Find
a) a fomula for z in terms of x and y,
b) the nterm of each sequence.

I can see the pattern in A, B & C but i just am not sure how to connect them.
 
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the nth term for each is givn below:
a(x): 3n
b(y): 30-2n
c(z): 11-0.5(n)

so...z = 11-0.5(n) = (22-n)/2 = (22-4n+3n)/2 = (22-4n +x)/2 = (8+22-2n-2n+x-8)/2
= (30-2n-2n+x-8)/2 = (y+x-2n-8)/2 = y/2 + x/2 - n -4 = z
 
There are many possible solutions.

For example z(x,y) = y/4 + 7/2 will also work just fine.
 
Thanks guys. For (a), my book said that the answer is z = \frac{1}{2}(52-x-y)
 

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