# Thread: Geometric Sequences

1. ## Geometric Sequences

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.

Determine the number of terms:

4, 12, 36, ... , 972
Now, I've tried this problem and this is what I did.
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?

2. wow... that makes me feel dumb. Ha ha. Well thank you very much. I guess I've been looking at sequences too long.

3. Originally Posted by Aerillious
wow... that makes me feel dumb. Ha ha. Well thank you very much. I guess I've been looking at sequences too long.
Don't worry. I made the same mistake not too long ago. That's how I recognized it so quickly.

-Dan

Edit: Ah well. "Against stupidity the gods themselves contend in vain."

4. the problem is you should have equated n - 1 = 5 ---> n = 6

as the formula is written here, we start with n = 1, not 0.

Geometric sequence:

$\displaystyle a_n = ar^n$ for $\displaystyle n = 0,1,2,3,4...$ .........here, (n + 1) gives the number of the term

or

$\displaystyle a_n = ar^{n - 1}$ for $\displaystyle n = 1,2,3,4...$ ................here, n gives the number of the term

you used the last formula, so starting at n = 1 was correct, the problem is you solved the first equation i mentioned incorrectly.

5. That makes a lot of sense, actually. Thank you. I think I need to get the hang of the difference between positive and negative sequences...

I'm really close to understanding it all, it's just a little elusive.