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Math Help - Find a formula for the sequence....

  1. #1
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    Find a formula for the sequence....

    The two questions are here, they're probably easy but I'm having a brain freeze lol

    http://img29.imageshack.us/img29/5626/file.png

    The 4(c) sequence is 5, 7, 9, 11....
    The 4(d) sequence is 5, -10, 20, -40.....
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  2. #2
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    Quote Originally Posted by brumby_3 View Post
    The two questions are here, they're probably easy but I'm having a brain freeze lol

    http://img29.imageshack.us/img29/5626/file.png

    The 4(c) sequence is 5, 7, 9, 11....
    The 4(d) sequence is 5, -10, 20, -40.....
    Hi brumby_3,


    1st one

    5,\ 7,\ 9,\ 11,......

    is an ARITHMETIC SEQUENCE.

    T_1=5,\ T_2=5+(1)2,\ T_3=5+(2)2,\ T_4=5+(3)2,\ T_5=5+4(2)...

    T_n=5+(n-1)2

    To sum all the terms of the sequence, the sum is

    S_n=\frac{T_1+T_n}{2}(n)

    which is the average value multiplied by the number of terms.

    S_n=\frac{5+5+(n-1)2}{2}(n)


    2nd one

    5,\ -10,\ 20,\ -40,.....

    The next term is the previous one multiplied by -2

    This is a GEOMETRIC SEQUENCE.

    T_1=5,\ T_2=(-2)5,\ T_3=(-2)^25,\ T_4=(-2)^35,...

    T_n=5(-2)^{n-1}

    The sum of these terms is

    S_n=\frac{5\left(1-(-2)^{n}\right)}{1-(-2)}

    which is \frac{a\left(1-r^n\right)}{1-r}

    where "a"=1st term, "r"=common ratio.
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