Definition: The common difference is the constant amount added to each term of an arithmetic sequence to get the next term; it equals any term minus the term before it.
What is it?
In an arithmetic sequence every step has the same size. That size is the common difference, written d. Positive d means the sequence climbs, negative d means it falls, and d = 0 gives a constant list.
How do you find d?
Subtract any term from the one after it: d = an+1 – an. Check at least two pairs to be sure the sequence really is arithmetic.
Example. For 83, 71, 59, 47: 71 – 83 = -12, 59 – 71 = -12, and 47 – 59 = -12. The common difference is -12. If you only know two distant terms, such as a3 = 14 and a8 = 39, divide the change by the number of steps: (39 – 14) / 5 = 5.
What should you watch for?
Always subtract in the same direction. Writing 59 – 71 for one pair and 71 – 59 for another gives signs that disagree. The common difference is also the slope of the line through the points (n, an).