A ball is dropped from a height of 24 m. With each bounce, the ball reaches a height that is half the height of the previous bounce. How far has the ball travelled by the time it comes to rest.
After 2 bounces: 24+12+12+6= 54m
There is a hint that says its a whole number
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This series goes like this- 24,12,12,6,6,3,3,1.5,1.5.......
Better write it by adding 2 consecutive terms i.e. 36,18,9,4.5,2.25...............
Basically, this series takes the form a, ar, ar², ar³ ....................
It has the summation a(r^n - 1)/(r-1) where n is the number of terms.
Rewrite this as ar^n/(r-1) - a/(1-r). Let r<1 and n be infinity. Then r^n is 0 and the formula simplifies to a/(1-r). So your answer is 36/(1-½) = 72 metres.
Better write it by adding 2 consecutive terms i.e. 36,18,9,4.5,2.25...............
Basically, this series takes the form a, ar, ar², ar³ ....................
It has the summation a(r^n - 1)/(r-1) where n is the number of terms.
Rewrite this as ar^n/(r-1) - a/(1-r). Let r<1 and n be infinity. Then r^n is 0 and the formula simplifies to a/(1-r). So your answer is 36/(1-½) = 72 metres.
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