Question

Identify the next three terms in the geometric sequence. 8, 24, 72, 216,...

Answer 1

Each term is being multiplied by three to get the next term in the sequence. So the answers are 648, 1944, 5832.

Answer 2

Comment
There are 2 ways to do this problem.
1. You can look at the next term to see how you got to it or
2. You can develop a formula to see what the next 2 terms are by solving the formula. 

In this case it is a geometric series. The easiest way is to find the ratio using t(n+1) / tn

Formula
t(n+1)/ t(n)

Substitute and solve
t_n+ 1 = 72
t_n = 24
t(n + 1) / f(n)  = 72/24 = 3

Try another example just to make sure.
t2 = 24
t1 = 8
t2 / t1 = 24/8 = 3

Find the next two terms
t_4 = 216
t_5 = 3 * t4
t_5 = 3 * 216
t_5 = 648  <<<<<<< Answer 1

t_6 = t5 * 3
t_6 = 648 * 3
t_6 = 1944   <<<<< Answer 2 

Method Two
Develop a formula. This has he advantage of not depending on previous answers.
tn = a1 * r^(n - 1)
a1 = 8
n = 5
r = 3

t5 = 8 * 3^4
t5 = 8 * 3*3*3*3
t5 = 8 * 81
t5 = 648

I'll set up the givens for t6. You know the answer. Try to get it.
t6 = ???
n = 6
a = 8
r = 3

See if you get 1944.