If the fifth term of a g.p. is 81 and second term is 24, find the g.p.

Use your definitions:
the fifth term of a g.p. is 81 ---> ar^4 = 81
second term is 24 -----> ar = 24

divide them:
(ar^4)/(ar) = 81/24
r^3 = 27/8
r = 3/2

then in ar=24
(3/2)a = 24
a = 16

the GP is
16, 24, 36, 54, 81, ...

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