Use the geometric mean to find the 7th term in a geometric sequence if the 6th term is 12 and the 8th term is 27.
a.18
b.19.5
c.20
d.17

A geometric sequence is when numbers in sequence have a common ratio. To solve this problem, we need for the geometric ratio for the sequence. Using the equation:

an=a1r^n-1

where is an is the number at an n term, r is the ratio and a1 is the first number of the sequence.

From the given numbers,

12 = a1 r^5
27 = a1r^7
 From the equations above,

a1 = 128/81
r = 3/2

Therefore, the 7th term is:

an = (128/81) (3/2)^6
an = 18