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A Conjecture
The answer depends on what the q pattern is.The answer depends on what the q pattern is.The answer depends on what the q pattern is.The answer depends on what the q pattern is.
7 Footnote: On the assumption that the segment shown will continue in the same pattern, 7 is obviously the answer sought. However, the statement of the problem gives no reason to make that assumption. Consequently, the segment may, in fact, continue as a repetition ( 10 1 9 2 8 3 10 1 9 2 8 3...) , in which case, the next numeral is 10. Furthermore, the segment may actually continue 3 3 3 3 3...in which case the next numeral is 3. Or--the segment may continue in any pattern at all, in which case, any numeral may be the actual element that is called for. In a word, the problem as stated does not allow a unique "correct" answer. (Credit Ludwig Wittgenstein for the analysis of problems of that kind.) Teachers and those who score standardized tests will not be amused by any effort to invoke that reasoning as an excuse for your not being able to come up with the expected answer: 7.
how many times does a pattern have to repeat
The lower extreme is the lowest number in a set of data* * * * *That is the correct conventional definition. However, for the mathematical definition you may have to allow for the fact that the lower extreme may not actually be attained: it may be an asymptotic value. For example, consider the set of numbers 1, 1/2, 1/4, 1/8 and so on. The sequence gets closer to 0 as you keep going but it is never actually equal to 0. The lower extreme of this infinite set is 0, but that is not an element of the set.