Hannah,
The three consecutive numbers could be represented using the format x-1, x and x+1 because they are all separated by a unit value of 1. Note also that x is the middle value of all three numbers.
Now going by the instructions given from the question, it says that the sum of the first and twice the second is 17 more than twice the third. This statement could be translated mathematically as:
(X-1) + 2X = 2(X+1) + 17
By expanding the brackets and adding the values, we get
3X - 1 = 2X +19,
Finally, by collecting the like terms, X=20. Therefore, the consecutive numbers would have to be X-1 which is 19, X which is 20 and X+1 which is 21