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Math Help - sequences help

  1. #1
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    sequences help

    hey everyone im new here and i've got a question which gives me the recursive definition of a sequence and I'm asked to find the nth term.
    here it is:
    Find a formula for the n-th term tn of the sequence (tn) defined by
    a) t1 = 3; tn = 3tn−1/2, n>=2.

    the next part is asking me to find the recursive definition of the formula:


    b) tn = 2 (n + 1)! 5n, n >=1.

    could someone take me through the steps rather than just posting the answer so I can do it myself the next time.
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  2. #2
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    Re: sequences help

    Quote Originally Posted by nehal234 View Post
    hey everyone im new here and i've got a question which gives me the recursive definition of a sequence and I'm asked to find the nth term.
    here it is:
    Find a formula for the n-th term tn of the sequence (tn) defined by
    a) t1 = 3; tn = 3tn−1/2, n>=2.

    the next part is asking me to find the recursive definition of the formula:


    b) tn = 2 (n + 1)! 5n, n >=1.

    could someone take me through the steps rather than just posting the answer so I can do it myself the next time.
    a)

    t_n= \frac{3^n}{2^{n-1}}=2 \cdot \left(\frac{3}{2}\right)^n
    Thanks from nehal234
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  3. #3
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    Re: sequences help

    thanks but could you show me how you reached that?
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  4. #4
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    Re: sequences help

    Quote Originally Posted by nehal234 View Post
    thanks but could you show me how you reached that?
    I simply wrote down a few first terms and deduced a general formula...
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  5. #5
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    Re: sequences help

    i've tried to input values into n such as 1 2 3 etc and i dont get the same values as if i put tn=1 2 3 etc
    t1=3
    t2=3/2
    t3=6/2
    t4=9/2

    is there something im dong wrong?
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  6. #6
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    Re: sequences help

    t_1=3

    t_2=\frac{9}{2}

    t_3=\frac{27}{4}

    t_4=\frac{81}{8}

    \vdots
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  7. #7
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    Re: sequences help

    i dont see why the base of 2 is being changed.
    also how do you out the formulas like how you are doing them?
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  8. #8
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    Re: sequences help

    Quote Originally Posted by nehal234 View Post
    thanks but could you show me how you reached that?
    Code:
    1        2          3          4  .........            n
    3 (3/2) 9/2 (3/2) 27/4 (3/2) 81/8 ......... (3/2) 3^n/2^(n-1)
    and 3^n / 2^(n-1) = 2*3^n / 2^n (as per princeps)

    Can also be shown as 2^(1-n)3^n
    Thanks from nehal234
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  9. #9
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    Re: sequences help

    i belive what the sequence means is that t1=3 then t2=(3*1)/2 and t3=(3*2)/2
    so i dont know how 27/4 81/8 and all of them come from
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  10. #10
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    Re: sequences help

    Quote Originally Posted by nehal234 View Post
    i belive what the sequence means is that t1=3 then t2=(3*1)/2 and t3=(3*2)/2
    so i dont know how 27/4 81/8 and all of them come from
    so you "think" 1st three terms are: 3, 3/2, 6/2
    That's NOT a geometric or arithmetic sequence

    Arithmetic and Geometric Sequences
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  11. #11
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    Re: sequences help

    Couldnít find any other suitable topic for my question
    I was looking at a roulette tips and tricks page but I couldnít find any maths sequence related advice. Can anyone please help me to determine what the roulette algorithms are and how maths can be applied to roulette? I know that thereís not special system, however Iím sure maths can resolve some probability questions in roulette?
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  12. #12
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    Re: sequences help

    could someone help me with part b) of this question?
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