Christina bought a yoyo from a company that claims that, with each retraction, the string rolls up by 70% of the original length. She sets up a tape measure and throws the yoyo 3 times. Her data are charted below.

Throw Length of string (feet)
1 3
2 2.1
3 1.47

Christina wants to find the sum of the length of string after 10 throws. What is the sum of the lengths, rounded to the nearest hundredth?

Question

Christina bought a yoyo from a company that claims that, with each retraction, the string rolls up by 70% of the original length. She sets up a tape measure and throws the yoyo 3 times. Her data are charted below.


Throw	Length of string (feet)
1	3
2	2.1
3	1.47


Christina wants to find the sum of the length of string after 10 throws. What is the sum of the lengths, rounded to the nearest hundredth?

tkhunny · Answer

1) Does70% prove to be correct?
2) Break out your best Geometric Series sum formula.

anonymous · Answer

idk??

tkhunny · Answer

Well, why not?

What's 70% of 3?

anonymous · Answer

2.1

anonymous · Answer

ahhh 0.121060821

tkhunny · Answer

Okay, you now have 10 throws to throw.

3 + 3*.7 + 3*.7^2 +...+ 3*.7^9

Is that 10 throws?  You have to believe.

anonymous · Answer

I believe ...!! praise the LAWD

anonymous · Answer

OMG THE SUM

tkhunny · Answer

Add them up:  $\dfrac{3 - 3*0.7^{10}}{1-0.7}$

This should be looking somewhat familiar.

anonymous · Answer

YES, IT DOES

ckaranja · Answer

This is a geometric series that follows a decreasing order. He simply should use 
$$ar^{n-1}$$
In this case a=3, r=$$\frac{ 2.1 }{ 3 }$$ and n=10
So,
$$(3*\frac{ 2.1 }{ 3})^{9}$$

tkhunny · Answer

@ckaranja Except that you probably should reread the problem statement.