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your very fist step is incorrect !!!The answer equation you have given is incorrect or you are missing something out of the question..
if T1 = 2 , then T2 = 2*0.75 or not? Just answer me this. If it is Then what I have done is correct.
Verify this for me.
a = 2
r = 3/4
n = n ?
a)
Sn = a(1-r^n)/1-r
Sn = 2(1-0.75^n)/1-0.75
Sn = 2-2(0.75^n)/0.25
Sn = 8-8(0.75^n)
b)
Sinf = a/1-r
Sinf = 2/1-0.75
Sinf = 8
Can't be greater than 8.
T2 will be 2*2*0.75 ... as it goesdown and re robounds ... exacly like mecahnice when it goes to max height