24 - 16 = 8
36 - 24 = 12
54 - 36 = 18
So, obviously, this isn't an arithmetic sequence.
24/16 = 3/2
36/24 = 3/2
54/36 = 3/2
Aha! This is a geometric sequence.
Now, let's find the 7th term in this sequence!
[tex]a_n = a_1 \cdot r^{n-1}[/tex]
We're trying to solve for a_7.
We know that a_1 is 16
We know that n = 7
We know that r = 3/2 or 1.5
Plug it in!
[tex]a_n = a_1 \cdot r^{n-1}\\\\a_7 =16 \cdot 1.5^{7-1}\\\\a_7 = 16 \cdot 1.5^6\\\\a_7 = 16 \cdot 11.390625\\\\\boxed{\bf{ a_7 = 182.25}}[/tex]
The seventh term is 182.25
