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=321331=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