# 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 $$a?$$

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