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Yes, the values are produced by a geometric series. For E6, the series has a ratio of R, where R^6 = 10, and the values are further rounded to two significant figures.

It's not just a geometric sequence that's convenient for base 10, it's the standard set of geometric sequences (that was chosen because they're convenient for base 10).

The caption on the graph (and the paragraph before the graph) directly addresses this: "This graph shows how any value between 1 and 10 is within ±10% of an E12 series value, and its difference from the ideal value in a geometric sequence."

It's a more accessible way of explaining it that doesn't require understanding geometric sequences first.

do geometric sequences care about the base?

The ones mentioned in the article return to powers of 10.

In contrast, musical notes don't, their frequencies return to powers of 2.