I notice that in current mathematics education they always have sections teaching about finding the missing member(s) of the sequences e.g. in this way:
$1,2,4,8,16$ , the next term is what?
Someone would argue that the next term is $32$ since they claim that the pattern of this sequences is about the non-negative integer powers of $2$ .
Someone would argue that the next term is $31$ since they claim that the pattern of this sequences is about the circle division by chords.
But in fact this type of questions are completely wrong since e.g. by the principle of interpolation, since we can find infinitely many numbers of the patterns of the existing terms, the values of other terms will be very depending on the patterns assumed and therefore have infinitely many possibilities, i.e. you can fill any values of other terms.
But the current mathematics education always assume this type of questions should have exact answers, that means they break the conscientiousness of mathematics.
Why the current mathematics education still hold this misleading education of the sequences?