There is only one type of arithmetic sequence.
The sequence may be defined by a "position-to-value" rule. This would be of the form:
U(n) = a + n*d
where a a constant which equals what the 0th term in the sequence would be,
d is also a constant - the common difference between each term in the sequence and the preceding term.
and n is a variable that is a counter for the position of the term in the sequence.
The same sequence can be defined iteratively by:
U(0) = a
U(n+1) = U(n) + d for n = 1, 2, 3, ...
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It is an arithmetic sequence for which the index goes on and on (and on).
That's an arithmetic sequence.
Arithmetic
It is an arithmetic sequence if you can establish that the difference between any term in the sequence and the one before it has a constant value.
No. An 'arithmetic' sequence is defined as one with a common difference.A sequence with a common ratio is a geometricone.