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Math Help - arithmentic sequence problem

  1. #1
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    arithmentic sequence problem

    hello

    here's the question I need a hand with, it's about arithmetic progressions:

    Find the first three terms of an arithmetic sequence where
    T5 (term 5)= 3xT2 and the sum of the sequence to six terms is 36

    any help is much appreciated so thanks in advance
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  2. #2
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    Tn = a + (n-1)d
    where a denotes first term and d denotes the common difference ( difference between any term and the previous term)

    so T2 = a + d
    T5 = a + 4d

    but T5 = 2*T2

    so a+4d = 2(a+d)

    which simplifies to a = 2d

    Sn the sum of n terms is given by

    Sn = n/2[2a+ (n-1)d]

    so S6 = 6/2[2a+5d] = 36

    so 6a + 15d = 36

    but a= 2d from above

    so 12d + 15 d = 27d = 36

    d = 4/3

    a = 2d = 8/3
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  3. #3
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    thanks so much for the help
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  4. #4
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    sorry!

    misread question

    T5 = 3T2

    so a+4d = 3a+3d

    Can you take it from here?
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  5. #5
    MHF Contributor
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    Quote Originally Posted by listeningintently View Post
    hello

    here's the question I need a hand with, it's about arithmetic progressions:

    Find the first three terms of an arithmetic sequence where
    T5 (term 5)= 3xT2 and the sum of the sequence to six terms is 36

    any help is much appreciated so thanks in advance
    Arithmetic sequence:
    Tn = T1 +(n -1)d
    Sn = (n/2)[T1 +Tn]

    T5 = 3(T2) .....given.
    T1 +(5 -1)d = 3[T1 +(2 -1)d]
    T1 +4d = 3T1 +3d
    4d -3d = 3T1 -T1
    d = 2T1 ---------------(1)

    S6 = 36 ...........given.
    S6 = (6/2)[T1 +Tn] = 36
    3[T1 +(T1 +(6-1)d)] = 36
    3[T1 +T1 +5d] = 36
    6T1 +15d = 36
    2T1 +5d = 12
    d = (12 -2T1)/5 -------(2)

    d = d,
    2T1 = (12 -2T1)/5
    10T1 = 12 -2T1
    12T1 = 12
    T1 = 1 ----------**

    So, d = 2T1 = 2(1) = 2

    Therefore,
    T1 = 1 -------------------answer.
    T2 = 1 +2 = 3 ------------answer.
    T3 = 1 +2(2) = 5 ----------answer.

    Check:
    T6 = 1 +5(2) = 11
    S6 = (6/2)[1 +11] = 3(12) = 36 .....OK.
    Last edited by ticbol; October 20th 2008 at 01:52 PM.
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