Question

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?

Answer 1

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 <i>difference</i> 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.

Answer 2

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?

Answer 3

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.

Answer 4

I’m sorry