Find c+f f the sum of any four consecutive numbers from a, 8, b, c, d, e, f, 2 is equal to 17

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Each entry in the list of numbers below is a Positive Integer:

a, 8, b, c, d, e, f, 2

If the sum of ANY four consecutive terms in the list is 17, what is the value of c + f?

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HINT : You are given that

  1. $a+8+b+c=17$

  2. $8+b+c+d=17$

  3. $b+c+d+e=17$

  4. $c+d+e+f=17$

  5. $d+e+f+2=17$

Can you use these to find $c+f$? For example if you subtract 2 from 1 you get $a=d$. When you subtract 5 from 4 you get $c=2$. Try playing around with these five equations.