Greenwood press

SEQUENCES
115
Old Faithful is a popular attrac-
tion at Yellowstone National Park,
because it is a very large geyser
and quite predictable. Source:
National Park Service photograph.

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twelve minutes, forming an arithmetic sequence of 46, 58, 70, 82, 94, . . . An erup-
tion of 
n minutes will indicate that the next eruption, a
n
, will occur in
a
n
= a
1
+ (n − 1)d minutes, where a
1
is the length after a one-minute eruption,
and
d is the constant difference of waiting time among eruptions that are a one-
minute difference in time. In this particular situation, the next eruption will occur
in
a
n
= 46 + (n − 1)12 minutes, if the previous eruption was n minutes long.
Harmonious chords produce another type of sequence. If you depress piano
keys for middle C, middle G, high C, and high E, then play low C, you will hear
the four other tones. If the string for low C is one meter long, then a string a half
meter long will sound a middle C, a one-third meter string would give middle G,
high C would be one-fourth meter, and high E would be one-fifth meter. The 
list of overtones is the sequence 
1,
1
2
,
1
3
,
1
4
,
1
5
, . . . which is called a harmonic
sequence. Any sequence that is formed from reciprocals of terms of an arithmetic
sequence is called harmonic. Harmonic sequences are important in the study of
magnetism, electricity, and the design of electric motors. Cosmologists studying
the origins of the universe look for harmonic patterns in microwave traces
received from space. 
online sources for further exploration
A demonstration that the harmonic series doesn’t converge

Artificial intelligence

Biological sequence alignment

DNA sequence database

Intensity, exposure, and time in photography

Iteration and recursion activities

Linear models

Musical scales


Predicting Old Faithful

Used car prices


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