Question

Please help, geometric series..

Finn bought a yoyo from a company that claims that, with each retraction, the string rolls up by 80% of the original length. He sets up a tape measure and throws the yoyo 3 times. His data are charted below.

Throw Length of string (feet)
1 3
2 2.4
3 1.92


Finn 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?

13.39 feet
15.00 feet
4.46 feet
0.40 foot

Answer 1

It's either A or B, right?

Answer 2

its A

Answer 3

yep, and any explanation needed? @breezy

Answer 4

yes, please

Answer 5

Thank you guys :)

Answer 6

Okay! Give me a second to type all of this and I'll explain c:

Answer 7

The formula for a the sum of a geometric sequence is \[\frac{ t _{1(r^n-1)} }{ r-1}\]

Answer 8

r equals common ratio
you get it by dividing term2 by term1

Answer 9

Makes sense now... Thank you!

Answer 10

n is the term you want to calculate to.
---
the r in the equation would be 4/5 3/2.4= 4/5
n is equal to 10.
---
find 4/5 to the 10th power then subtract one and multiply t1 to it.
the bottom is 4/5-1 and divide the top by bottom, and there's the answer!

Answer 11

and yw <3 GL!