Various progressions

Algebra Level 3

3 rational numbers \(a,\) \(b,\) and \(c\) form a geometric progression in that order.

  • \(a,\) \(b+8,\) and \(c\) form an arithmetic progression in that order.
  • \(a,\) \(b+8,\) and \(c+64\) form a geometric progression in that order.

If \(a\) is an integer, then what is \(a?\)


Source: FFJM's semi-finals
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