I'm having trouble getting the number of terms for the sum of this geometric progression.

This question has been making me mad all day! It's in a advanced maths text book and my teacher asked us to do it for homework.
Here's the question:

How many terms of the sequence 4, 3, 2.25, ... can you add before the sum exceeds 12?

Here's my working out:

The answer I got is n=-2 and it's incorrect. I checked the answer for this question at back of text book and it was n=4. I tried and tried but still got n=-2. Please help!

Answer

Hint. From the line

$$1-\left(\frac34 \right)^n>\frac34$$ you get $$\left(\frac34 \right)^n<\frac14$$ giving $$n>\frac{\log(1/4)}{\log(3/4)}=4.8\ldots$$ that is $$n=5.$$