Summation Notation

[thunc14]

So this isn't Calculus specifically just basic summation notation, so forgive me if this is the wrong subsection. Here's the problem:

A ball starts at an initial height of 1.5 meters above the ground. Each time the ball bounces, it reaches 80% of its previous height. Which of the following accurately reflects the total distance the ball has bounced after 5 bounces? Please only consider the distance that the ball is traveling downward.

I attached the answer choices.

I eliminated B and C off the bat, since multiplying by .2 is not correct. However, I feel that the answer is E, none of the above, because the summation must start at 1.5, which A gives, but it must bounce 5 times, not 4 as in choice A. Am I looking at this problem the wrong way?

 

[lev888]

So this isn't Calculus specifically just basic summation notation, so forgive me if this is the wrong subsection. Here's the problem:

A ball starts at an initial height of 1.5 meters above the ground. Each time the ball bounces, it reaches 80% of its previous height. Which of the following accurately reflects the total distance the ball has bounced after 5 bounces? Please only consider the distance that the ball is traveling downward.

I attached the answer choices.

I eliminated B and C off the bat, since multiplying by .2 is not correct. However, I feel that the answer is E, none of the above, because the summation must start at 1.5, which A gives, but it must bounce 5 times, not 4 as in choice A. Am I looking at this problem the wrong way?

How many terms are there? Note the first and last values of k.

 

[thunc14]

There would be 5 terms.
1. 1.5m fall then first bounce.
2. 1.2m fall then second bounce
3. 0.96m fall then third bounce
4. 0.768m fall then fourth bounce
5. 0.6144m fall then fifth bounce

So the answer would be A then

 

[Dr.Peterson]

A ball starts at an initial height of 1.5 meters above the ground. Each time the ball bounces, it reaches 80% of its previous height. Which of the following accurately reflects the total distance the ball has bounced after 5 bounces? Please only consider the distance that the ball is traveling downward.

There would be 5 terms.
1. 1.5m fall then first bounce.
2. 1.2m fall then second bounce
3. 0.96m fall then third bounce
4. 0.768m fall then fourth bounce
5. 0.6144m fall then fifth bounce

So the answer would be A then

I agree.

But the problem is poorly written, as it first asks the trickier problem, "the total distance the ball has bounced after 5 bounces", and then takes it back and tells you not to think about the total distance at all, but only "the distance that the ball is traveling downward". I had my mind all geared up to see if you'd missed the trick in the question, then they went and made it easy ... apart from interpreting the summation notation, which apparently was their only concern.