Math
posted by Amy .
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)=63=3
S(3)S(2)=116=5
S(4)S(3)=1811=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=31=2
S(2)2²=64=2
S(3)3²=119=2
S(4)4²=1816=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=31=2
S(2)2²=64=2
S(3)3²=119=2
S(4)4²=1816=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.