2003 AMC 12B Problems/Problem 6
The second and fourth terms of a geometric sequence are 2 and 6. Which of the following is a possible first term?
Solution
Call the first term and the common ratio
. Then the nth term is given by
. Therefore,
and
. Substituting 2 and 6 for
and
respectively gives
and
. Dividing the first equation by the second gives
, so
Substituting this into the first equation gives
. Dividing by
and rationalizing the denominator gives
. The negative value corresponds to answer choice