Note II. — Increasing series only will be considered in this book, as
rules that apply to increasing series apply to decreasing series also, pro-
vided that, wherever the common difference is introduced, it is used with
the contrary sign.
488. To FIND AKT Term in a Sebies, when the First
Tebm, Common Difference, and Number of Terms

are 6IYEN.
Let 5 = first term^ 2 = common difference, and 6= the nmnber of
terms. The series will be constructed as follows : —

ao

1st term. 2d term. 3d term. 4th term. 5th term. 6th term.
5. 6 + 2. 6 + 2X2. 5 + 3X2. 6 + 4X2. 6 + 5X2.
We find that the second term equals the first term, plus the common
difference ; the third term equals the first term, plus two times the com-
mon difference ; the fourth term equals the first term, plus three times
the common difference, &c. ; and that the last or sixth term equals the
first term, plus five times the common difference. Hence,

I. To find any term of the series : Add the first term to the
product of the common difference multiplied hy the number of
terms which precede it,

U. To find the last term: Add the first term to the product of
the common difference multiplied hy the number of terms less otie.
ARITHMETICAL PROGRBSSlON. ^7;

Examples.
1. In an increasing series the first term is 4, and the common
difference is 8 ; what is the seventh term ? Ans, 52.
