Math

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I need some help with these quesitons

1. a1 = -1, and an = 4/3an-1 for n = 2, 3, 4, ___. What is the common ration, r, for this sequence?

2. A rubber ball is dropped from a height of 50 ft. Assume that each bounce of the ball is vertical and that each bounce reaches a height of 5/6 of the maximum height of the previous bounce. What is the total distance traveled throughout the lifetime of bounces for this ball?
I'm not sure I even understand this question

3. The following infinite geometric series will have a finite sum: 1001/6, 1001/36, 1001/216, 1001/1296
true?

  • Math -

    1. since An = 4/3 An-1
    An/An-1 = 4/3
    That's r

    #2. You should place it in the obvious context of geometric sequences
    a = 50
    r = 5/6
    S = a/(1-r)

    #3. What is r?
    Divide any term by the previous one.
    If |r| > 1, the infinite sum is finite.

  • Math -

    So I'm getting false for #3...

  • Math -

    For the 2nd one I'm getting 299..however my answer choices are 500, 450, 280, or the ball travels an infinite distance

  • Math -

    The ball falls 50', and then starts bouncing.
    Then it goes up and down on each 5/6 height bounce So that's a total of twice the Sum from then on. So, skipping the first term

    S = 2*(50 * 5/6) /(1 - 5/6) = 500

    This is almost a trick question. The immediate temptation, if the question is not read carefully, is just to say, Oh. S = 50/(1-5/6). But then they threw in the condition that you only count the bounces, and you have to recall that each complete bounce has an up and a down journey. I'm surprised that 600 was not one of the choices. It'd be an obvious but easy error to make.

    #3. Eh? r = 1/6
    each denominator is 6 times the previous one.

    Did you do as I suggested?

    r = A3/A2 = 1001/216 / 1001/36
    = 1001/216 * 36/1001 = 1/6

    Good luck on that SAT. You appear to have a long way to go.

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