Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 decade ago

5th grade math problem: if set 1 has 3 dots, set 2 has 6, and set 3 has 10, how many does set n=100 have?

my spouse came up with 5151 by counting *every* single set, but there HAS to be a formula.

6 Answers

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  • 1 decade ago
    Favorite Answer

    S1 = 3

    S2 = 3 + 3

    S3 = 3 + 3 + 4

    S4 = 3 + 3 + 4 + 5

    ...

    Sn = 3 + 3 + 4 + 5 + ... + (n+1)

    Sn = 3 + (3+n+1)*(n-1)/2

    Sn = (6 + (n+4)*(n-1))/2

    Sn = (n^2 + 3n + 2)/2

    S100 = (100^2 + 3*100 + 2)/2

    = (10000 + 302)/2

    = 10302/2

    = 5151

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  • Euro
    Lv 4
    1 decade ago

    Your spouse counted correctly. There is a simple formula.

    It is ((n+1)*(n+2))/2

    so for 100 it is

    (101*102)/2 = 10 302/2 = 5151

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  • 1 decade ago

    s(1) = 1+2

    s(2) = 1+2+3

    s(3) = 1+2+3+4

    .

    .

    s(n) = (n+1)(n+2)/2

    s(100) = 101 * 102 / 2 = 5151

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  • 1 decade ago

    the differences grow by a fixed amount - so this is a quadratic sequence with a general formula t(n)=an^2+bn+c

    t(1)=3=a+b+c

    t(2)=6=4a+2b+c

    t(3)=10=9a+3b+c

    t(3)-t(2)=5a+b=4

    t(2)-t(1)=3a+b=3

    t(3)-2t(2)+t(1)=2a=1

    a=0.5

    t(3)-t(2)=5*0.5+b=4

    b=4-2.5=1.5

    t(1)=0.5+1.5+c=3

    c=3-2=1

    so the specific formula is:

    t(n)=0.5n^2+1.5n+1

    and

    t(100)=5000+150+1=5151

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  • Anonymous
    1 decade ago

    Yeh Dj is right.

    There's no formula to this because there is no connection between (sets 1 & 2) and (set 3). I would not classify this as 5th grade math unless set 3 equalled 9 dots.

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  • 1 decade ago

    did u make a mistake in writing that question or did u miss out on any information because the common ratio isnt the same.....set 1 has 3 dots set 2 has 6 dots and set 3 has 10 dots....ther is no way of finding out how many set 4 has....

    edit: damn....wasnt i rong....are u sure thats 5th grade maths man?? check out the posts bellow me!! thats geometric and arthmetic stuff...you dont do that in 5th grade!!

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