(In reply to
My revised solution by Ady TZIDON)
Ady,
Both 2016 and 1007, 1009 are members of a (finite) arithmetic progression (or sequence), by definition. They also fit the definition you provided: sequence of numbers such that the difference of any two successive members of the sequence is a constant. The definition of "any" does not discount the possibility of no members or no other members in the sequence, though it usually does imply at least one. The actual definition of a finite arithmetic sequence does not limit a sequence to three members. Even the empty set is considered valid  though it is often excluded by some, and for the solution to this problem it would also be excluded as the empty set would definitely have no member where its sum totals 2016. I can see the argument to exclude 2016 as a solution, yet  except by an interpretation of your definition of an arithmetic sequence  I can not see the exclusion of 1007, 1009.
Edited on January 24, 2015, 6:51 am

Posted by Dej Mar
on 20150124 04:51:45 