1987 AMC 12 Problem 9

Attempt Problem 9 of the 1987 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1987 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

The first four terms of an arithmetic sequence are

a,

x,

b,

2x.

The ratio of

a

b

\frac14

\frac13

\frac12

\frac23

2

Write all four terms using

a

and a common difference

Use the equation relating the second term

x

to the fourth term

2x

Let the common difference be

d.

Then

x=a+d,\ b=a+2d,

and

2x=a+3d.

Thus

2(a+d)=a+3d,

a=d

and

b=3d.

Therefore

\frac{a}{b}=\frac{1}{3}.

Thus the correct answer is B.

Problem 9 in other years