January 2014
Intermediate to advanced
144 pages
4h 2m
English
Content preview from Mathematical Formulas for Industrial and Mechanical Engineering
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term a
n11
5 a
n
r is called an geometric sequence, a
n
5 nth term and r 5 common
ratio.
The nth or general term of an geometric sequence is given by a
n
5 ar
n21
, where
a is the first term.
Examples The general (nth) term for 2, 6, 18, 54, ... is a
n
5 a
1
(3)
n21
and the first
term is 2.
5.23 The Finite Geometric Series
If a
n
5 ar
n21
is a geometric sequence then the sum of the sequence is
S
n
5
X
n
i51
a
n
5 a
1 2 r
n
1 2 r
Example 3 1 6 1 12 5 21. This is a geometric series with common ratio 2, where
a 5 3, a
n
5 12, r 5 2.
S
n
5 3
1 2 2
3
1 2 2
5 3
27
21
5 3ð7Þ5 21
5.24 The Infinite Geometric Series
If a
n
5 ar
n21
is a geometric sequence and jrj, 1 then the sum of the infinite
sequence
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