Page:Elementary algebra (1896).djvu/319

CHAPTER XXXIV.

Arithmetical, Geometrical, and Harmonical Progressions.

364. A succession of quantities formed according to some fixed law is called a series. The separate quantities are called terms of the series.

Arithmetical Progression.

365. Definition. Quantities are said to be in Arithmetical Progression when they increase or decrease by a common difference.

Thus each of the following series forms an Arithmetical Progression:

${\begin{aligned}&3,7,11,15,\dots \\&8,2,-4,-10,\dots \\&a,a+d,a+2d,a+3d,\dots .\\\end{aligned}}$

The common difference is found by subtracting any term of the series from that which follows it. In the first of the above examples the common difference is 4; in the second it is —6; in the third it is $d$.

366. The Last, or nth Term, of an A. P. If we examine the series

$a,a+d,a+2d,a+3d,\dots$

we notice that in any term the coefficient of d is always less by one than the number of the term in the series.

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