I'm having a little trouble understanding this stuff. Sequences in general, really, but I've chosen a geometric one to list here.

It's a rather simple question but I can't seem to find anything that answers it.

Now, I've tried this problem and this is what I did.Determine the number of terms:

4, 12, 36, ... , 972

Tn = ar^n-1

= 972 = 4(3)^n-1

= 243 = 3^n-1. [243 = 3^5]

Therefore 3^n - 1 = 3^5

There are five numbers in the term.

That's what I've done, yet my textbook tells me that the answer is actually six. I have no idea how they got that and I'm beginning to suspect a typo. Any help?