Question

Can someone please figure this out???

Answer 1

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