write the first five terms of a geometric sequence whose first term is 100 and whose third term is less than 30

Answer 1

100r^2 < 30
r < √0.3 = 0.547722

so, one sequence would have r=.5:
100 50 25 12.5 6.25 ...

If r=.5477, we have
100 54.77 29.997 16.429 8.999 ...
The 3rd term is just less than 30.