# Number patterns

1. Oct 29, 2004

### footprints

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.

2. Oct 29, 2004

### imranmeghji

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

3. Oct 29, 2004

### uart

There are many possible solutions.

For example z(x,y) = y/4 + 7/2 will also work just fine.

4. Oct 29, 2004

### footprints

Thanks guys. For (a), my book said that the answer is $$z = \frac{1}{2}(52-x-y)$$

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