Truth Tellers Progression?

Algebra Level 4

Consider an infinite geometric progression will all real terms satisfying at least one of the following

  • The sum of all the terms of this progression is 1.
  • The sum of every second term of this progression is 2.
  • The sum of every third term of this progression is 3.

Exactly how many of these statements is/are true?

1 2 3

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