Is this the true definition of the recursive equation an = an - 1 + d?

';The value of any term in the arithmetic sequence is the value of the previous term minus some variable amount d.';Is this the true definition of the recursive equation an = an - 1 + d?
An arithemetic progression = a + (a + d) + (a + 2d) + . . . + (a + (n-1)d)





The general term, a(n) = a + (n-1)d





The recursive formula = the previous term + the common difference (the common difference can have a negative value).





The previous term is usually denoted by a(n-1)


(n-1 written as subscript).





So the third term, recursively, would be written a(2) + d