Answer:
T2 = 7.5
T3 = 22.5
T4 = 67.5
Step-by-step explanation:
The nth term of a GP series is Tn = ar^(n-1), where a = first term and r = common ratio = Tn/Tn-1.
a = 2.5
T1 = 2.5 => 2.5r^0 = 2.5
T5 = 202.5 => 2.5r^4 = 202.5
=> r^4 = 202.5/2.5
=> r^4 = 81
=> r^2*r^2 = 9*9
=> r^2 = 9
=> r = 3
Therefore,
T2 = (2.5)(3)^1 =(2.5)(3) = 7.5
T3 = (2.5)(3)^2 =(2.5)(9) = 22.5
T4 = (2.5)(3)^3 =(2.5)(27) = 67.5
