Question

Insert three geometry means between 1 and 81. I can't even solve it.

Answer 1

remember the terms of a geometric sequence run like this:
a ar ar^2 ar^3 ...

so we
1 , r, r^2, r^3, 81

term(5) = 81
r^4 = 81
r = ± 3

so the sequence is
1, 3, 9, 27, 81
or
1, -3, 9, -27, 81