MATH EXPONENTIAL HELP?

2. How many terms are there in the sequence: 10, -6, 18/5, -54/25, .... -4374/15625 ?

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  • Alan
    Lv 7
    3 months ago
    Favourite answer

    So this is geometric series 

    -6/10  = -3/5

    18/5 / -6   = -18/30 =-3/5 

    so r = -  3/5  

    a(1) = 10 

    so standard formula is 

    a(n) = a(1)*r^(n-1) 

    a(n) =  10*(-3/5)^(n-1)   

    so the last term is 

    -4374/15625  = 10*(-3/5)^(n-1) 

    since it is negative 

    n-1 = odd 

    so n = even 

    This allow to remove the -1 

    -4374/15625 = 10*(-1)^(odd n-1) (3/5)^(n-1)  

    -4374/15625 = -10* (3/5)^(n-1)  

    divide both sides by -10 

    4374/156250 = (3/5)^(n-1)  

    take ln of both sides

    ln(4374/165250) =  (n-1)*ln(3/5) 

    (n-1) =   ln(4374/156250)/ ln(3/5)  

    n-1 = 7 

    n = 7+1 = 8 

    n = 8  

  • sepia
    Lv 7
    3 months ago

    How many terms are there in the sequence: 

    10, -6, 18/5, -54/25, .... -4374/15625

    a_n = -2 (-1)^n 3^(n - 1) 5^(2 - n) 

     -4374/15625 = -2 (-1)^n 3^(n - 1) 5^(2 - n) 

    Integer solution:

    n = 8

  • rotchm
    Lv 7
    3 months ago

    Work at it a little longer and try to find a pattern. 

    Here, convince yourself that this sequence can be written as

    (-1)^0 * 2* 3^0 / 5^(-1), (-1)^1 * 2* 3^1 / 5^0, (-1)^2 * 2* 3² / 5^1, (-1)^3 * 2 * 3^3 / 5² ...

    See the pattern?

    You can also simplify this a little if need be. Write it with the parameter "n".

    Ok...   -2 * 25 / 3 * (-3/5)ⁿ

    If n=1 you get? If n=2 you get? Does it generate your sequence?

    So, how many terms are there ?

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