It is an ordered set of elements. These elements may or may not be numbers, there may or may not be a defining rule - for example a sequence of random numbers.
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That refers to a sequence of numbers, one after the other, determined by some rule.
It is the sequence of first differences. If these are all the same (but not 0), then the original sequence is a linear arithmetic sequence. That is, a sequence whose nth term is of the form t(n) = an + b
Well, it would depend what the sequence was...? If the sequence was 2,4,6,8,10,12,14,16,18,20, then the 9th term would be 18!
That depends what the pattern of the sequence is.
An infinite sequence.
I don't think such a term is used in calculus. Check the spelling. Perhaps you mean point of inflection?