Greenwood press

SERIES
119

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trees is used for wood each year, then the forest will reach its ideal level of 
80,000 trees in about seven years, since 
500(1
−0.9375
7
)
1−0.9375
> 28, 000, the number of
trees lost in the fire.
Arithmetic series are used when consecutive values have a constant differ-
ence. The sum of the first 
n terms of the series, s
n
, is determined by the equa-
tion
s
n
= (a
1
+ a
n
)

n
2
 or s
n
= (2a
1
+ (n − 1)d)

n
2
 . For example, the sum 
of the first one hundred positive integers is generated by the series 
1 + 2 + 3 +
. . . + 100. This is an arithmetic series with n = 100 terms, a
1
= 1, and a
100
=
100. Therefore the sum of this series, s
100
= (1 + 100)

100
2
 = 5, 050. Drilling
and mining operations use arithmetic series to determine the total distance their
machines will need to drill when excavating rock from the earth. Suppose a con-
struction team is hired to dig a hole that has a cross-sectional area of 10 square
meters and will be 50 meters deep. Suppose that the drilling machine moves 2
feet downward when digging in the earth’s surface, and then stops to allow
workers to remove the 20 cubic meters of loose dirt. Therefore the first drilling
attempt will be 2 meters deep, the second drilling attempt will be 4 meters deep,
the third drilling attempt will be 6 meters deep, and so on for a total of 25 trips.
In this situation, the drilling machine and the dirt from the ground will need to
be moved a total of 650 meters in order to dig a 50 meter hole, since
(2 • 2 +
(25 − 1)2)

25
2
 = 650. The mining or construction company can then use this
information to determine its fees based on the total distance it will need to move
dirt out of the hole.
online sources for further exploration
Buying on credit

Drug dosage



Geometric series applications

Loan or investment formulas

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