Find the missing terms of the geometric sequence.

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

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