anonymous one year ago 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?

1. tkhunny

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

2. anonymous

idk??

3. tkhunny

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

4. anonymous

2.1

5. anonymous

ahhh 0.121060821

6. tkhunny

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.

7. anonymous

I believe ...!! praise the LAWD

8. anonymous

OMG THE SUM

9. tkhunny

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

10. anonymous

YES, IT DOES

11. ckaranja

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, $(3*\frac{ 2.1 }{ 3})^{9}$

12. tkhunny

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