Posted by **Amy** on Monday, October 11, 2010 at 6:36pm.

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?

- Math -
**MathMate**, Monday, October 11, 2010 at 7:16pm
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.

- Math -
**Amy**, Monday, October 11, 2010 at 7:27pm
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?

- Math -
**MathMate**, Monday, October 11, 2010 at 7:31pm
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.

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