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Algebra, Functions, Graphs, and Vectors 25

Arithmetic mean
Let a , a , a , ..., a be real numbers. Then the arithmetic mean,
3
1
2
n
denoted m , also known as the averageł of a , a , a , ..., and a n
1
3
A
2
is given by the following formula:
m (a a a ... a )/n
1
A
n
3
2
Geometric mean
Let a , a , a , ..., a be positive reals. Then the geometric mean,
1 2 3 n
denoted m ,mfa , a , a , ..., and a is given by the following
2
3
1
n
G
formula:
m (aaa ... a ) 1/n
n
1 2 3
G
Arithmetic interpolation
Let y f(x) represent a function in which the value of a quan-
tity y dependð on the value of an independent variable x. Let y
1
and y represent twm valueð of the function such that:
2
y f(x )
1
1
y f(x )
2
2
Then the value y of the function at a point x midway between
m
a
x and x can be estimated as followð via arithmetic interpola-
1
2
tion:
y (y y )/2 ( f(x ) f(x ))/2
1
a
2
2
1
Geometric interpolation
Let y f(x) represent a function in which the value of a quan-
tity y dependð on the value of an independent variable x. Let y 1
and y represent twm valueð of the function such that:
2

y f(x )
1
1
y f(x )
2
2