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They are antonyms. Following means coming after. Preceding means coming before.
The next number is 13, the total of the two numbers preceding it.
I'm going to assume by "most probable answer" you mean the next term? The next term is 63. The pattern in this sequence is to add the preceding number to the current number to get the next number. For example, to get to 9, you add 3 to 6. To get to 15, you add 6 to 9 and so on and so forth.
The sequence 0112358 represents the Fibonacci sequence, where each number is the sum of the two preceding ones. The next number in this sequence is 13, as it is the sum of the last two numbers, 5 and 8. Thus, the next number is 13.
preceding EOT succeeding E10