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.