(39 points plz )find the sum of a finite geometric series. a ball is dropped from a height of 10 meters. each time it bounces, it reaches 50 percent of its previous height. the total vertical distance the ball has traveled when it hits the ground the fifth time is

So we need to find the sum of the first 5 terms.

You have told me that the first term is 10 meters, and that r = 0.5 per term.

With this knowledge, we can use the formula s_n=a₁((1-r^n)/(1-r)).

Plugging in the terms that we know...

s₅=10((1-0.5⁵)/(1-0.5))

s₅=10(0.96875/0.5)

s₅=10(1.9375)

s₅=19.375

With s₅, we can determine that the ball has traveled a total of 19.375 meters after 5 bounces.

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.