## 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.