Problem:
The first three terms of a geometric progression are 3​,33​, and 63​. What is the fourth term?
Answer Choices:
A. 1
B. 73​
C. 83​
D. 93​
E. 103​
Solution:
Each term in a geometric progression is r times the preceding term. The ratio is
r=321​331​​=331​−21​=3−61​
Thus the third term is correctly given as r⋅331​=3−61​⋅331​=361​, and the fourth term is r⋅361​=3−61​⋅361​=30=1​.
The problems on this page are the property of the MAA's American Mathematics Competitions