What is the 6th term of the geometric sequence where a1=1024 and a4=-16

We have to solve for the common ratio first ...

The rule for a geometric sequences is:

a (n) = ar^ (n-1) and we are given two terms so we can say:

-16/1024 = (ar^3) / (ar^0)

-16/1024=r^3

r = (-1/64) ^ (1/3)

r=-1/4 so

a (n) = 1024 (-1/4) ^ (n-1)

a (6) = 1024 (-1/4) ^5

a (6) = - 1

A1=1,024

a2=-256

a3=64

a4=-16

a5=4

a6=-1