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Math Help - Can any 1 help on SEQUENCES?

  1. #1
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    Can any 1 help on SEQUENCES?

    Hi all i have these two problems that have been bothering me , any 1 know how to solve it please

    1. A string vibrates 30mm in the first oscillation and subsequently 90 % of its previous value in each succeding ocsillation. How many oscillation will it take before the vibration falls below 10mm and how far will it have vibrated in this time?

    2. The sum of the first n terms of a geometric series is

    1/3 - 2^n/3^n+1

    Find
    ii) The first term
    ii) the second term
    iii) the common ratio
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  2. #2
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    1. You have a = t_1 = 30 and each time you have 90\% of your previous value, so the common ratio r = 0.9.

    You should know that t_n = ar^{n-1}, so t_n = 30\cdot 0.9^{n-1}.

    So if t_n < 10 then that means

    30\cdot 0.9^{n-1} < 10.

    Solve for n, you will need to use logarithms.
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  3. #3
    MHF Contributor Also sprach Zarathustra's Avatar
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    2.

    i) a_1=? (put n=1 in your sum formula)
    ii)a_2=? (put n=2 into sum formula, but you get the sum of two elements a_1+a_2, what you should do? hint: use i) )
    iii)q=a_(n+1)/a_(n)=a_2/a_1
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