Question 794180
Let the seven numbers be represented by
(1) {a,b,c,d,e,f,g} and 
let sum(b-f) be the sum of numbers b through f.
For the average of the first six we have
(2) (a + sum(b-f))/6 = 40 or
(3) (a + sum(b-f)) = 240  
We are given that the first number, a, is 55, so we have
(4) sum(b-f)) = 240 - a or
(5) sum(b-f)) = 240 - 55 or
(6) sum(b-f)) = 185
Now for the average of the last six numbers we have
(7)(sum(b-f) + g)/6 = 35 or
(8)(sum(b-f) + g) = 210 
Now use (6) in (8) to get
(9) 185 + g = 210 or
(10) g = 210 - 185 or
(11) g = 25
Answer: The first number is 55 and the last number is 25, giving an absolute difference of 30.
PS We have no idea what the five in between numbers are!