Question #00f85

1 Answer
Jan 12, 2018

If by exponential you mean they can be written in the form
#y=a^x# then yes.

Explanation:

Geometric sequences are categorised as such because their sequential terms differ by a common ratio.
eg. #2,4,8,16,32,64,128,...#

This is exactly the same at the exponential relationship;
#y=2^x#

Another way of thinking about this is by observing the interchangeability of the recursive and explicit definitions of geometric progressions.

eg. for a geometric progression with a starting term #a# and a common ratio #r# the recursive definition is;
#T_(n+1)=rxxT_n#
#T_1=a#
and the corresponding explicit definition is;
#T_n=axxr^(n-1)#

I hope this helps :)