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Math Help - Sequence and Series Question

  1. #1
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    Sequence and Series Question

    Hey everyone. I haven't been on in quite some time, but I guess that was due to not having school, although I do think I should've helped out those who had similar problems as I did, but I am sorry. Anyways, I just started Precalculus, and I had a question that I was quite confused on. Well anyway, here goes....

    How many terms are in the sequence 4,7,10.....40?

    Now i know I could do this the long way by doing it manually, but I forget the formula or way to do it to get it in a much simpler way. I would appreciate anyone that can help me with this and bid you all a good day.

    Edit: I also forgot that I put this in the wrong section with elementary/middle school math questions, when it belongs in the high school math section, namely in Pre-Calculus, so I am sorry about that.
    Last edited by Norman Smith; September 8th 2007 at 11:54 AM. Reason: I wrote this topic in the wrong section.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Norman Smith View Post
    Hey everyone. I haven't been on in quite some time, but I guess that was due to not having school, although I do think I should've helped out those who had similar problems as I did, but I am sorry. Anyways, I just started Precalculus, and I had a question that I was quite confused on. Well anyway, here goes....

    How many terms are in the sequence 4,7,10.....40?

    Now i know I could do this the long way by doing it manually, but I forget the formula or way to do it to get it in a much simpler way. I would appreciate anyone that can help me with this and bid you all a good day.

    Edit: I also forgot that I put this in the wrong section with elementary/middle school math questions, when it belongs in the high school math section, namely in Pre-Calculus, so I am sorry about that.
    These are incrementing by 3 at each step, and the n-th term is 1+3n.

    If N is the number of terms then:

    1+3N=40,

    so:

    N=39/3=13.

    RonL
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  3. #3
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    How many terms are in the sequence 4,7,10.....40?

    Let's see how the sequence goes.
    1st term = 4
    2nd term = 7
    2nd term minus first term, 7-4 = 3

    3rd term is 10
    3rd term minus 2nd term, 10 -7 = 3

    Umm, the sequence is Arithmetic. The common difference between terms is 3.

    a2 = a1 +d
    a3 = a2 +d = a1 +d +d = a1 +2d = a1 +(3-1)d
    ....
    an = a1 +(n-1)d

    So, since a1 = 4 and an = 40, and d=3, then,
    40 = 4 +(n -1)(3)
    (n-1) = (40 -4)/3
    n -1 = 12
    n = 12 +1 = 13

    Therefore, there are 13 terms in that sequence.
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  4. #4
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    Well thank you both for the help, and I sincerely appreciate it, and also understand it, however I am having difficulty with another problem.

    It states: Cylindrical tiles of uniform size are stacked in the form of a triangle. There are 21 tiles on the bottom row. Find the total number of tiles in the stack.


    Last edited by Norman Smith; September 8th 2007 at 08:08 PM.
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  5. #5
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    Post new questions in a new thread.

    Stack something.

    1 gives 1
    Put that 1 on two others. That's three.
    Make a base 3 wide and move the first three on top. That's six.

    Now what?
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  6. #6
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    Quote Originally Posted by Norman Smith View Post
    Cylindrical tiles of uniform size are stacked in the form of a triangle. There are 21 tiles on the bottom row. Find the total number of tiles in the stack.
    This sequence is the same as the first one.
    Here,
    a1 = 21
    an = 1
    d = -1

    That is if the tiles are stacked up in such as way that a tile is resting on two tiles below it. That is, the center of the tile above is aligned to the meeting of the two tiles below.
    a1 = 21
    a2 = 20
    a3 = 19
    .
    .
    an = 1

    So, again,
    an = a1 +(n-1)d
    1 = 21 +(n-1)(-1)
    1 = 21 -n +1
    n = 21 +1 -1
    n = 21

    Then, the sum of an Aritmetic series is
    Sn = (n/2)(a1 +an)
    So,
    S21 = (21/2)(21 +1)
    S21 = 21(11)
    S21 = 231

    Therefore, there are 231 tiles in the stack. ------answer.
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