2003 AMC 10B Problem 8

Problem 8 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 terms be

a,

ar,

ar^2,

ar^3,

\dots

with

ar=2

and

ar^3=6.

Dividing gives

r^2=3,

r=\pm\sqrt3.

Then

a=\dfrac{2}{r}=\pm\dfrac{2}{\sqrt3}=\pm\dfrac{2\sqrt3}{3}.

The choice

-\dfrac{2\sqrt3}{3}

matches the negative case. Thus, the correct answer is B.

Concepts: geometric sequence · radical

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