Math

posted by mysterychicken

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?

  1. Steve

    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.

  2. mysterychicken

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

  3. mysterychicken

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

  4. Steve

    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.

Respond to this Question

First Name

Your Answer

Similar Questions

  1. math

    5. A rubber ball dropped on a hard surface takes a sequence of bounces, each one 3/5 as high as the preceding one. If this ball is dropped from a height of 15 feet, what is the total distance it has traveled after it hits the surface …
  2. Advanced Functions

    I need help answering these questions 1. State the Common Ratio of the following Geometric sequence 3/4 , 3/10 , 3/25 , 6/125 2. In the Arithmetic Sequence below, X = ___ 100 , ___ , _X_ , 64 3. For the Geometric Sequence below, X …
  3. math

    Find the missing numbers to complete the patterns. Some are arithmetic and some are geometric. State the commom differences or common ratio. 1) 1,2,___,___,___,32 2)800,80,8,0,8,0.08,___,____ Some tricky ones that don't follow the …
  4. Math

    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?
  5. physic PLEASE I REALLY NEED HELP WITH THIS PROBLEM

    Two identical rubber balls are dropped from different heights. Ball 1 is dropped from a height of 100 feet, and ball 2 is dropped from a height of 210 feet. Write a function for the height of each ball. h1(t) = h2(t) = When does ball …
  6. college algebra

    A rubber ball is dropped from the top of a hole.Exactly 3.0 seconds later, the sound of the rubber ball hitting bottom is heard.How deep is the hole?
  7. math

    Two identical rubber balls are dropped from different heights. Ball 1 is dropped from a height of 156 feet, and ball 2 is dropped from a height of 202 feet. Write a function for the height of each ball. h1(t)=159+t h2(t)=202+t
  8. Physics

    A rubber ball with a mass of 0.130 kg is dropped from rest. From what height was the ball dropped, if the magnitude of the ball's momentum is 0.710 kg ยท m/s just before it lands on the ground?
  9. Math

    When dropped on a hard surface, a rubber ball takes a series of bounces, each one about 4/5 as high as the preceding one. If the rubber ball is dropped from a height of 20 ft, what is the approximate distance the ball travels before …
  10. Math

    1. Find all values of p so that 6p, 4p-1, p^2 - 1 will be an arithmetic sequence. 2. The common ration of a geometric sequence is -3. IF the terms of this sequence are 3y, y+6, z+1, ..... respectively, what is the value of z?

More Similar Questions