Greenwood press

114
SEQUENCES

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nth year
value ($)
1
20,000.00
2
16,000.00
3
12,800.00
4
10,240.00
5
8192.00
6
6553.60
7
5242.88
8
4194.30
9
3355.44
10
2684.35
The estimated values of an automobile with a new price of $20,000 
and depreciating 20 percent each year.
The twelve tones in an octave form a geometric sequence so that the end of
an octave has a frequency twice that of its low tone. High C (512 cps) is twice
middle C (256 cps). The multiplication of frequencies is a constant ratio across
the octave, so each multiplication must be the twelfth root of 2, or about 1.059.
So if A is 440 cps, the next key, B-flat, will be 440 •1.059 ≈ 466 cps. (See Ratio.)
Old Faithful is a popular attraction at Yellowstone National Park, because the
geyser produces long eruptions that are fairly predictable. When tourists visit Old
Faithful, they will see a sign that indicates an estimated time that the geyser will
next erupt. No one controls the geyser like an amusement park ride. Instead, its
patterns over time have caused park rangers to develop predictable eruption times
using an arithmetic sequence. The time between eruptions is based on the length
of the previous eruption. If an eruption lasts one minute, then the next eruption
will occur in approximately forty-six minutes (plus or minus ten minutes). If an
eruption lasts two minutes, then the next eruption will occur in approximately
fifty-eight minutes. This pattern continues based on a constant difference of