Question

The end of a spring is pulled as far as it will go and then is released. On the first bounce back it extends 135 cm. On its second bounce back it extends 45 cm. On its third bounce back it extends 15 cm. How many times will the spring bounce back before it extends 5/9 cm?

I have no idea how to solve this problem. Could someone please show me the steps?

Answer 1

Tn = 135/3^(n-1)

5/9 = 135/3^(n-1)
3^(n-1) = 135*9/5 = 81
since 3^4 = 81, n=5

So, on the 5th bounce it will extend 5/9 cm

Answer 2

It's not the 6th bounce? Because when I put 6 into the equation I got 5/9