Geometric sequences and series

A geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio, r.

an=an1roran=a1rn1


Example

Write the first five terms of a geometric sequence in which a1=2 and r=3.

We use the first given formula:

a1=2

a2=23=6

a3=63=18

a4=183=54

a5=543=162

Just as with arithmetic series it is possible to find the sum of a geometric series. It is found by using one of the following formulas:

Sn=a1a1rn1rorSn=a1(1rn)1r


Video lesson

Use the formula for the sum of a geometric series to determine the sum when a1=4 and r=2 and we have 12 terms.