Question

Jessa bought a yoyo from a company that claims that, with each retraction, the string rolls up by 60% 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 1.8 3 1.08 Jessa 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?

Answer 1

Answer:

The sum is 7.45

Step-by-step explanation:

Every time she throws a yoyo, the new length is 60% of the original, so we can calculate the length of the yoyo in the n throw as:

$L_1=3(0.6)^{0}=3\\L_2=3(0.6)^{1}=1.8\\L_3=3(0.6)^{2}=1.08\\L_n=3(0.6)^{n-1}$

Then, the sum of the n terms is a geometric serie because every term has the form:

$a(r)^{n-1}$

Where a is equal to 3, r is equal to 0.6 and n goes from 1 to 10

Therefore, the sum of the n terms can be calculated as:

$S_n=a*\frac{1-r^{n} }{1-r}$

So, the sum of the length of string after 10 throws is:

$S_{10}=3*\frac{1-0.6^{10} }{1-0.6}=7.45$