Geometric and Exponential Sequences are the Same

A geometric sequence is any sequence such that the nth term is of the form
$a_n=ar^{n-1}$
where
$a$
is the first term and
$r=\frac{a_{n+1}}{a_n}$
is the ratio of successive terms, called the common ratio.
An exponential sequence is a sequence of the form
$a_n=Ae^{k(n-1)}$
where
$A, \; k$
are constants.
We can write
$A(e^k)^{n-1}$
which is a geometric sequence with first term
$A$
and common ratio
$e^k$

Hence geometric and exponential sequences are the same thing, and so are exponential growth and geometric growth.

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