Problem:
The second and fourth terms of a geometric sequence are 2 and 6. Which of the following is a possible first term?
Answer Choices:
A. β3β 
B. β323ββ 
C. β33ββ 
D. 3β 
E. 3 
Solution:
Let the sequence be denoted a,ar,ar2,ar3,β¦, with ar=2 and ar3=6. Then r2=3 and r=3β or r=β3β. Therefore a=323ββ or a=β323ββ.
Answer: Bβ.
The problems on this page are the property of the MAA's American Mathematics Competitions