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Math Help - Solving a sequence question simultaneously

  1. #1
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    Solving a sequence question simultaneously

    Hi

    Question: I have to find the common difference and the first term when T8= 21 and T20= 105.

    What I have done is state the rule : a + (n-1)d

    Then came up with the equations a= 19x + 105 and a= 7x + 21
    In y = mx +c form:

    Then I obtained the common difference: 19d + 105 = 7d+ 21
    19d +84 = 7d
    12d+84
    d = 7
    And then I tried to get to get the first term by subtituting 7 into equation however this did not work:


    I got the common difference correct but not the first term, can someone explain what I did incorrectly.


    Help is greately respected and appreciated

    Thank you
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  2. #2
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    Quote Originally Posted by atom360 View Post
    Hi

    Question: I have to find the common difference and the first term when T8= 21 and T20= 105.

    What I have done is state the rule : a + (n-1)d

    Then came up with the equations a= 19x + 105 and a= 7x + 21
    In y = mx +c form:

    Then I obtained the common difference: 19d + 105 = 7d+ 21
    19d +84 = 7d
    12d+84
    d = 7
    And then I tried to get to get the first term by subtituting 7 into equation however this did not work:


    I got the common difference correct but not the first term, can someone explain what I did incorrectly.


    Help is greately respected and appreciated

    Thank you
    n = 8: 21 = a + 7d .... (1)

    n = 20: 105 = a + 19d .... (2)

    (2) - (1): 84 = 12d => d = 7.

    Substitute d = 7 into either (1) or (2) and solve for a.
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