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Each number is half the previous number. The series formula is a(n) = 32 *(½)n⁻¹ 32, 16, 8, 4, 2, 1, 0.5 The next three numbers in the sequence are : 0.25, 0.125, 0.0625
The next number in this sequence is 65. according to your numbers ( 2 5 11 20 32 47 ) you add 3 to get 5 from 2. then you add 6 to 5 in order to get 11. then you'll add 9, 12, 15 ( then add 18 to 47 and get 65 ) etc. Each time you add you must increase the added by 3. BTW i really enjoyed your question. Hope this helps. :)
The differences are not the same so the sequence is not arithmetic. The sequence starts with a zero, so it cannot be geometric, or an exponential (power) sequence. The quartic: (2n4 - 19n3 + 64n2 - 83n + 36)/6 fits the 5 points. That gives the next term as 55.