This is not an arithmetic sequence. All arithmetic sequences have a common difference. Every term has a constant difference to the term before it.
In this case...
-3-2=-5
4.5--3=7.5 so there is no common difference.
All geometric sequences have a common ratio, each term is a constant ratio when compared to the previous term...this is a geometric sequence because:
-3/2=4.5/3=-6.5/4.5=-3/2 or -1.5 This is the common ratio.
This sequence can be expresses as
(-3/2)(an)=a(n+1)
However we normally express a geometric sequence as:
a(n)=ar^(n-1), where a is the first term, r is the common ratio, and n is the term number...
We have a=2, r=-3/2 and we want to know the 15 term...
a(15)=2(-3/2)^14=4797969/8192
