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
1. since An = 4/3 An-1
An/An-1 = 4/3
#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.
So I'm getting false for #3...
For the 2nd one I'm getting 299..however my answer choices are 500, 450, 280, or the ball travels an infinite distance
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.