GEOMETRIC PROGRESSIONS

A series of quantities is said to be in geometrical progression when each term is formed from the preceding term by multiplying by a constant factor which may be positive or negative. This constant factor is called the common ratio (r). Examples:

• Given the g.p. 2, 4, 8, 16, 32 then r = 2
• Given the g.p. 4, -2, 1, -0.5, 0.25 then d = -0.5

Thus the terms of a g.p. are:

a, ar, ar^2, ar^3, Etc.

To find the nth term of a g.p.

• The 1st term is a.
• The 2nd term is ar.
• The 3rd term is ar^2.
• The 4th term is ar^3.

and so the nth term of a g.p. is ar^(n-1). Letting Tn stand for the nth term we have:

Where:

• a = The first term
• r = The common ratio

This is the standard form of a g.p.

Created and maintained by Frans Coenen. Last updated 11 October 1999