2003 AMC 12B Problem 6

Problem 6 of 25EasierAlgebra

The second and fourth terms of a geometric sequence are

2

and

6.

Which of the following is a possible first term?

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Solution

Let the first term be

a

and the common ratio

r.

Then

ar = 2

and

ar^3 = 6,

r^2 = 3

and

r = \pm\sqrt{3}.

The first term is

a = \frac{2}{r} = \pm\frac{2}{\sqrt{3}} = \pm\frac{2\sqrt{3}}{3}.

The choice

-\dfrac{2\sqrt{3}}{3}

appears among the options. Thus, the correct answer is B.