Math

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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 -

    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 -

    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 -

    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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