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 ti…

Question

asked Mar 6, 2017 13.8k views

2 Answers

FarshidABZ · Answer 1 · 2017-03-11T12:42:00+0000

Answer:

The sum is 7.45

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:

$S_n=a*(1-r^(n) )/(1-r) \\$

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

$S_(10)=3*(1-0.6^(10) )/(1-0.6)=7.45 \\$