Geometric Sequence

Suppose that a, b and c is a geometric sequence, and a>b>c, then a/b=b/c.

a/b=b/c

For example, 1, 7 and 49 is a geometric sequence. The next number can be obtained by multiplying its previous number by a particular number, that is, the common ratio of the geometric sequence.

g(2)^(2) = g(1) · g(3) , g(2) · g(3) = g(1) · g(4) , g(2) · g(4) = g(1) · g(5) , ...

Arithmetic Sequence

Suppose that a, b and c is an arithmetic sequence, and a>b>c, then a-b=b-c. They have a common difference, and let the common difference be x, then x=a-b=b-c. For example, 1, 2 and 3 is an arithmetic sequence, and their common difference is 2-1 as well as 3-2, that is, 1.

2· a(2) = a(1) + a(3) , a(2) + a(3) = a(1) + a(4) , a(2) + a(4) = a(1) + a(5) , ...