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. −3​
B. −323​​
C. −33​​
D. 3​
E. 3
Solution:
Let the sequence be denoted a,ar,ar2,ar3,…, with ar=2 and ar3=6. Then r2=3 and r=3​ or r=−3​. Therefore a=323​​ or a=−323​​​.
The problems on this page are the property of the MAA's American Mathematics Competitions