Answer Box

Answer to Query
"Will such geometric sequences be exponential functions?"
(geometric sequences whose graphs increase or decrease)

Let's look at the formulas for an geometric function and for an exponential function.

Geometric Sequence:

funcgeographpicA

Exponential Function: f (x) = a• b^x

Geometric Function:
n is the variable
(variable is an exponent)
r is the common ratio
f (1) is a constant.

Linear Function:
x is the variable
(variable is an exponent)
b is growth/decay factor
a is a constant.

By renaming of "parts", it can be seen that these function have the same form:
f (n) = f (1) • r^n-¹
f (x) = a • b^x-¹ which is the same form as f (x) = a • b^x
Geometric sequences whose graphs increase (or decrease) are exponential functions.