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=an−1⋅roran=a1⋅rn−1
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=2⋅3=6
a3=6⋅3=18
a4=18⋅3=54
a5=54⋅3=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=a1−a1⋅rn1−rorSn=a1(1−rn)1−r
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.