make a sketch of the first few bounces and you will see:
1 bounce --- 56 m
2nd bounce = 2(28) = 56
3rd bounce = 2(14) = 28
4th bounc = 2(7) = 14
5th bounce = 2(3.5) = 7
6th bounce = 2(1.75) = 3.5
add them up to get ..... 164.5
or:
from the 2nd on , we have a geometric sequence with
a = 56, r = 1/2
We need the sum of
1st term + 5 terms of the GS
= 56 + 56(1 - (1/2)^5)/(1 - 1/2)
= 56 + 56( (31/32) / (1/2) )
= 56 + 56(31/16)
= 56 + 217/2
= 164.5