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Let’s see if I can show why sequence questions are no good.
The problem with sequence questions is that any answer is in fact a correct answer. Of course, in answering a sequence question, we need to find the most obvious answer. But the issue of “the most obvious answer” is never (or rarely) clarified. Given the sequence 4, 7, 10, 13, 16, 19, 22, the determination of what the next term of the sequence is depends on what mechanism (or formula) generated the first seven terms of the sequence in the first place. And there are infinitely many formulas that can generate the first seven term sof the sequence as given. So, which of these infinitely many formulas did the inquirer have in his/her mind? Of course, for the given sequence, many believe that the simplest mechanism that can generate the sequence is the arithmetic process. But how in general are we supposed to know what the simplest mechanism that generates any given sequence is? The issue is: what does "simplest" mean anyway?
To bring home the problem with sequence questions, let me give you three questions and see if you can answer them:
(1) Find the next four terms in the following sequence:
252, 140, 70, 30, 10, 2, ?, ?, ?, ?
(2) Find the next term in the following sequence:
3, 2, 3, 3, 5, 7, 3, 5, 11, 7, ?
I really would have failed easily answering either one of the preceding questions? I don’t like them unless certain sufficient clues are given along with the question. And here’s one of my favorite (really??) sequence questions:
(3) Find the next three terms of the following sequence:
0, 0, 0, 0, ?, ?, ?
Is there a mensa who'd like to crack it open? Good Luck!
The problem with sequence questions is that any answer is in fact a correct answer. Of course, in answering a sequence question, we need to find the most obvious answer. But the issue of “the most obvious answer” is never (or rarely) clarified. Given the sequence 4, 7, 10, 13, 16, 19, 22, the determination of what the next term of the sequence is depends on what mechanism (or formula) generated the first seven terms of the sequence in the first place. And there are infinitely many formulas that can generate the first seven term sof the sequence as given. So, which of these infinitely many formulas did the inquirer have in his/her mind? Of course, for the given sequence, many believe that the simplest mechanism that can generate the sequence is the arithmetic process. But how in general are we supposed to know what the simplest mechanism that generates any given sequence is? The issue is: what does "simplest" mean anyway?
To bring home the problem with sequence questions, let me give you three questions and see if you can answer them:
(1) Find the next four terms in the following sequence:
252, 140, 70, 30, 10, 2, ?, ?, ?, ?
(2) Find the next term in the following sequence:
3, 2, 3, 3, 5, 7, 3, 5, 11, 7, ?
I really would have failed easily answering either one of the preceding questions? I don’t like them unless certain sufficient clues are given along with the question. And here’s one of my favorite (really??) sequence questions:
(3) Find the next three terms of the following sequence:
0, 0, 0, 0, ?, ?, ?
Is there a mensa who'd like to crack it open? Good Luck!