Page:Elementary algebra (1896).djvu/319

 CHAPTER XXXIV.

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

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:

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

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. 301