What is an common difference?

Answer 1

A common difference is a mathematical concept that appears in arithmetic sequences. An arithmetic sequence is a sequence of numbers, U(1), U(2), ... generated by the following rule:

U(1) = a

U(2) = U(1) + d

U(3) = U(2) + d

and, in general,

U(n) = U(n-1) + d

that is, you have a starting number a and, after that, each term in the sequence is found by adding a fixed number, d, to the previous term in the sequence.

An equivalent formulation is U(n) = a + (n-1)*d

The difference between any two consecutive terms is d and this is the common difference.

For example, in the sequence 3, 7, 11, 15, 19, .... the common difference is 4.

This is because 7-3 = 4

11-7 = 4

15-11 = 4 and so on.