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. Choose the answer that shows the sum of the lengths rounded to the nearest hundredth.

A. 0.03 foot
B. 2.50 feet
C. 7.50 feet
D. 7.45 feet

Answer 1

The general formula for a geometric sequence can be written as: 
a(n) = a r^(n-1) 

a = first term = 3 
r = common ratio = 0.6 
n = number of terms = 10

substituting the values:

a(n) = 3 * (0.6)^(10-1)
a(n) = 3 * (0.6)^9 
a(10) = 0.030

Sum of the ten terms = 3 (1-0.6^10)/1-0.6
                                   = 2.98/0.4
                                   = 7.45

Answer 2

Answer:

D) 7.45 feet

Explanation: