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?

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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?

Mathematics
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1) Does70% prove to be correct? 2) Break out your best Geometric Series sum formula.
idk??
Well, why not? What's 70% of 3?

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2.1
ahhh 0.121060821
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.
I believe ...!! praise the LAWD
OMG THE SUM
Add them up: \(\dfrac{3 - 3*0.7^{10}}{1-0.7}\) This should be looking somewhat familiar.
YES, IT DOES
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, \[(3*\frac{ 2.1 }{ 3})^{9}\]
@ckaranja Except that you probably should reread the problem statement.

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