Infinite geometric series help...?

Question

A rocket is launched into the air so that it reaches a height of 200m in the first second. Each subsequent second it gains 6% less height. How do I find out how high the rocket will climb?

Answer 1

3333.33(recurring)m, assuming deceleration only due to friction and not gravity. gravity would just make it messy...

Answer 2

200 + 200(0.94) + 200 (0.94)^2 + ...

= 200/(1-0.94)

= 200/0.06

= 3333 1/3

Answer 3

a , ar ,ar^2 , ar^3 , ar^4................ is a geometric series

sum of infinite terms of a geometric series  = a/(1 - r)

first term = a = 200

second term = a - 6%a  =  94a/100  = a(94/100)  =  a*r

common ratio = r = 94/100

Sum  = 200(1 - 94/100) =  20000/6  =  10000/3 metres