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An arithmetic sequence is a sequence of numbers where the difference between successive terms is a constant. Using $a$ for the first term and $d$ for the difference, the sequence is then: * $a,~a+d,~a+2d,~a+3d,~a+4d,~\ldots$ Counting $a$ as term number 1, or the first term, we can see that * term number 2 is $a+d,$ or $a+1d,$ * term number 3 is $a+2d,$ * term number 4 is $a+3d,$ and so on. The multiplier is always one less than number of the term. Thus the $n^{th}$ term is $a+(n-1)d.$ Compare with * Geometric sequence * General sequence