The characteristic of geometric sequences is that any term divided by the previous term is a constant, called the common ratio. Each term in this sequence is 2 times the previous term. In this case the sequence is an=2(2)^x.
If it were an arithmetic sequence any term subtracted by the previous term would be constant, called the common difference.
The total number of cups for younger kids is 3.66 and for the older kids its 7.5 so if you add those together it is about 11.16 which is less than 12 cups, so your answer is yes she does have enough