COMC 2015 B Problem 3

An arithmetic sequence is a sequence where each term after the first is the sum of the previous term plus a constant value. For example, 3,7,11,15, \ldots is an arithmetic sequence.

S is a sequence which has the following properties:

  • The first term of S is positive.
  • The first three terms of S form an arithmetic sequence.
  • If a square is constructed with area equal to a term in S, then the perimeter of that square is the next term in S.

Determine all possible values for the third term of S.