Representing terms as a/r, a, ar gives product a³ = -1, so a = -1. Using sum -1/r – 1 – r = 13/12 gives common ratio r = -3/4 or -4/3, yielding terms 4/3, -1, 3/4 or 3/4, -1, ...
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Starting with 30 bacteria and doubling factor 2, the count after n hours is 30 x 2ⁿ. Thus, after 2 hours there are 120, after 4 hours 480 and after n hours 30 x 2ⁿ.