Definition: A sequence is arithmetic if the differences between consecutive terms are the same. Thus the sequence a(1), a(2), a(3) ....... a(n).... is arithmetic if there is a number d such that a(2) -a(1)=d, a(3) -a(2) =d, and a(4) - a(3) =d and so on. The number D is the common difference of the arithmetic sequence.
Geometric sequences:
A sequence is geometric if the ratios of consecutive terms aren't the same
A(2)/a(1) = r, a(3) / a(2) = r, a(4) / a(3) = r.... (R cannot = 0)
The number are is the common ratio of the sequence
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