Step 1 = 3 boxes

Step 2 = 6 boxes
Step 3 = 11 boxes
Step 4 = 18 boxes

How many boxes at step 50?
Which one?
100, 102, 2500, 2502

How would I solve this?

S(1)=3

S(2)=6
S(3)=11
S(4)=18

We note that S(2)-S(1)=6-3=3
S(3)-S(2)=11-6=5
S(4)-S(3)=18-11=7
Thus the difference increases uniformly. This is an indication that term n is related to the square of the number of terms, n.

Try
S(1)-1²=3-1=2
S(2)-2²=6-4=2
S(3)-3²=11-9=2
S(4)-4²=18-16=2

So the hypothesis that S(1) is related to the square of n is true, namely
S(n)=n²+2

So figure out which answer is correct.

For 3, 5, 7 increases by 2

so in the equation this is (+2)

or is does that mean that n is squared?

and S(1)-1²=3-1=2
S(2)-2²=6-4=2
S(3)-3²=11-9=2
S(4)-4²=18-16=2 this determines that it is (+2)in the equation?

or the other way around?

S(4)-4²=2

or
S(4)=4²+2, and in general,the rule is:
S(n)=n²+2

Check for cases n=2,3 and 4.

I’m sorry

To solve this problem, we can see that the number of boxes at each step is increasing by a specific pattern. Let's try to identify the pattern first:

Step 1 = 3 boxes
Step 2 = 6 boxes = 3 + 3
Step 3 = 11 boxes = 6 + 5
Step 4 = 18 boxes = 11 + 7

By observing the pattern, we can see that each step is adding an increasing odd number to the previous step:

Step 1 to Step 2: Addition of 3 (odd)
Step 2 to Step 3: Addition of 5 (odd)
Step 3 to Step 4: Addition of 7 (odd)

Based on this pattern, we can determine how many boxes there will be at Step 50 by adding an increasing odd number to the number of boxes at Step 49.

We know that at Step 49 there are 18 + 7 = 25 boxes (based on the pattern).

Now, to find the number of boxes at Step 50, we need to add an increasing odd number to the number of boxes at Step 49. In this case, the next odd number would be 9.

Step 49 to Step 50: Addition of 9 (odd)

Therefore, the number of boxes at Step 50 would be 25 + 9 = 34 boxes.

Now, let's consider the given answer choices: 100, 102, 2500, and 2502.

Since we determined that at Step 50 there will be 34 boxes, we can conclude that the answer is neither 100 nor 102.

Additionally, since the given answer choices are quite large numbers, it is unlikely that the number of boxes will reach such large quantities by Step 50. Therefore, we can eliminate 2500 and 2502.

Therefore, the correct answer is 34 boxes.