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Math Help - confusing >.<

  1. #1
    Newbie dizzycarly's Avatar
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    confusing >.<

    I am really stuck on a question..

    (Q) Find x from the following:

    34.56, x, 24, 20.

    The asnwer is 28.80. I don't know how to get that. The two fomula you can use are Tn = a+(n-1)d or Sn= n/2 [2a+(n-1)d]

    Thanks if you can show me how to do it!
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by dizzycarly View Post
    I am really stuck on a question..

    (Q) Find x from the following:

    34.56, x, 24, 20.

    The asnwer is 28.80. I don't know how to get that. The two fomula you can use are Tn = a+(n-1)d or Sn= n/2 [2a+(n-1)d]

    Thanks if you can show me how to do it!
    Could you please write the problem exactly as it appears in the book? This would help me to better understand the problem.

    Do you mean T_n=a+(n-1)d or S_n= \frac{n}{2}[2a+(n-1)d]

    If so, what do t, s, a, and d represent?
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  3. #3
    Super Member
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    Quote Originally Posted by dizzycarly View Post
    I am really stuck on a question..

    (Q) Find x from the following:

    34.56, x, 24, 20.

    The asnwer is 28.80. I don't know how to get that. The two fomula you can use are Tn = a+(n-1)d or Sn= n/2 [2a+(n-1)d]

    Thanks if you can show me how to do it!
    The two formulas you wrote are for use with arithmetic sequences, but the sequence you wrote is a geometric sequence.

    In any event, x = 28.80 because the ratio between two consecutive terms is constant:
    \frac{34.56}{28.8} = \frac{28.8}{24} = \frac{24}{20} = 1.2.


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  4. #4
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by yeongil View Post

    In any event, x = 28.80 because the ratio between two consecutive terms is constant:
    \frac{34.56}{28.8} = \frac{28.8}{24} = \frac{24}{20} = 1.2.


    01
    Dude, you're like some kind of wizard.
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  5. #5
    MHF Contributor
    Grandad's Avatar
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    Ap/gp

    Hello dizzycarly
    Quote Originally Posted by dizzycarly View Post
    I am really stuck on a question..

    (Q) Find x from the following:

    34.56, x, 24, 20.

    The asnwer is 28.80. I don't know how to get that. The two fomula you can use are Tn = a+(n-1)d or Sn= n/2 [2a+(n-1)d]

    Thanks if you can show me how to do it!
    The formulae you quote are related to Arithmetic Progressions - where the differences between consecutive terms are equal. The difference between 24 and 20 is -4, and obviously this can't be the difference between 34.56 and x, and x and 24.

    So we must look elsewhere.

    In fact, this is a Geometric Progression, where the ratio of consecutive terms is constant. You do it like this:

    The ratio of 24 to 20 is \frac{24}{20} : 1  = 1.2:1. In other words, we must multiply 20 by 1.2 to make 24. If this sequence is a GP, we shall be able to multiply 24 by 1.2 to get x, and then multiply x by 1.2 to get 34.56. And this works!

    Try it out: 24\times 1.2 = 28.8, and 28.8 \times 1.2 = 34.56.

    So x = 2.8.

    (In fact, the common ratio of a GP is the ratio that will take you from left to right through the sequence of numbers; in this case that's the ratio the other way round; i.e. 20:24, or \tfrac56:1.)

    Grandad
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