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Math Help - sequences

  1. #1
    Senior Member euclid2's Avatar
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    sequences

    1.
    A) -16,-8,-4,-2,-1
    B) 3,9,27,81,243
    C) 16,-8,4,-2,1
    D) 3,1.5,0.75,0.375,0.1875

    Find an expression for the general term for each of the geometric sequences

    2.

    determine t3,t5, and tn for the geometric sequences with properties below

    A) a=5x and r=2x
    B) t6=6 and t4=24

    How would i create a spreadsheet and graph for 3B)

    Thank you
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  2. #2
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    In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed non-zero number called the common ratio. For example, the sequence 2, 6, 18, 54, ... is a geometric progression with common ratio 3. Similarly 10, 5, 2.5, 1.25, ... is a geometric sequence with common ratio 1/2. The sum of the terms of a geometric progression is known as a geometric series.
    Thus, the general form of a geometric sequence is
    and that of a geometric series is
    where r ≠ 0 is the common ratio and a is a scale factor, equal to the sequence's start value. - Wikipedia.


    A) -16,-8,-4,-2,-1
    to find common ratio, divide your second term by the first term. or divide your third term by your second term and so on..
    thus, r = -8/-16 = -4/-8 = -2/-4 = -1/-2 = 1/2.

    now that you have your common ratio r and your first term a,
    the formula for geometric progression is


    now your a=-16 and r=1/2
    so the expression for the general term for this geometric progression is
    = -16[(1/2)^(n-1)]


    same goes for question b c and d..and question 2 too!
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