Answer
The sequence is geometric.
The common ratio is $e^2$.
Work Step by Step
A geometric sequence has a common ratio $r$. The common ratio is multiplied to the current term to get the next term of the sequence.
The common ratio is equal to the the quotient of a term and the term before it.
Solve for the ratio of each pair of consecutive terms. USe the rule $\dfrac{a^m}{a^n} = a^{m-n}$ to obtain:
$\dfrac{e^4}{e^2} = e^{4-2} = e^2
\\\dfrac{e^6}{e^4}=e^{6-4} = e^2
\\\dfrac{e^8}{e^6} =e^{8-6} = e^2$
The consecutive terms have a common ratio so the sequence is geometric.
The common ratio is $e^2$.
