A series of quantities is said to be in arithmetical progression when each term is formed from the preceding term by adding a constant quantity which may be positive or negative. This constant quantity is called the common difference (d). Thus:
| Common difference d | = | 2nd term - 1st term |
| = | 3rd term - 2nd term | |
| = | 4th term - 3rd term | |
| Etc. |
Examples:
Thus the terms of an a.p. are:
a, a+d, a+2d, a+3d, Etc.
Therefore the nth term of an a.p. is a + (n-1)d. Letting Tn stand for the nth term we have:
Where:
This is the standard form of an a.p.
Created and maintained by Frans Coenen. Last updated 15 February 2001