The nth term of an arithmetic sequence
= a + [(n - 1) X d]
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Add a constant number to one term to find the next term
It is a sequence of numbers. That is all. The sequence could be arithmetic, geometric, harmonic, exponential or be defined by a rule that does not fit into any of these categories. It could even be random.
A(1) = 12A(4) = 3 A(10) = -15.
Without further terms in the sequence, it is impossible to determine what the rule in the sequence is.
You take the difference between the second and first numbers.Then take the difference between the third and second numbers. If that difference is not the same then it is not an arithmetic sequence, otherwise it could be.Take the difference between the fourth and third second numbers. If that difference is not the same then it is not an arithmetic sequence, otherwise it could be.Keep checking until you think the differences are all the same.That being the case it is an arithmetic sequence.If you have a position to value rule that is linear then it is an arithmetic sequence.