The height of a plant after each of the first three weeks was 7mm, 20mm, and 33mm, respectively. If this pattern of growth continues, in what week will the plant be more than 100mm tall? 

The answer is 9 weeks. 

This is what I did, and it's clearly wrong: 
tn = 7 + (n-1)13 
tn = 7 + 13n - 13 
tn = 13n - 6 

100 = 13n - 6 
100 + 6 = 13n 
106/13 = n 
I get a crazy decimal (8.1538....) which shouldn't be the answer... 

What am I doing wrong, and how do you properly answer this question?

Thanks very much in advance!

To properly answer this question, let's analyze the growth pattern of the plant.

From the given information, we can see that the height of the plant is increasing by 13mm each week. In the first week, the height is 7mm, in the second week it is 20mm, and in the third week it is 33mm.

We can express this pattern mathematically as follows:
h(n) = 7 + 13(n-1)

Where h(n) represents the height of the plant in the nth week.

To find out in which week the plant will be more than 100mm tall, we need to solve the following equation:
7 + 13(n-1) > 100

Let's solve this equation step by step:

7 + 13(n-1) > 100
13(n-1) > 100 - 7
13(n-1) > 93
n-1 > 93/13
n > 93/13 + 1

Now, let's calculate:

93/13 = 7.1538...

Adding 1, we get:
n > 7.1538 + 1
n > 8.1538

Since n represents the number of weeks and it cannot be a fraction, we need to round up to the nearest whole number. Therefore, the plant will be more than 100mm tall in the 9th week.

So, the correct answer is indeed 9 weeks.