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Algebra Difficulty 1.0 Junior Prove it Canada

Determine all possible values of $r$ such that the three term geometric sequence $4, 4r, 4r^2$ is also an arithmetic sequence.
(An arithmetic sequence is a sequence in which each term after the first is obtained from the previous term by adding a constant. For example, $3, 5, 7, 9, 11$ is an arithmetic sequence.)

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.