1950 AMC 12 Problem 5

Attempt Problem 5 of the 1950 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 1950 AMC 12 solutions, or check the answer key.

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If five geometric means are inserted between

8

and

5832,

the fifth term in the geometric series is:

648

832

1168

1944

None of these answers

Inserting five means makes the given numbers the first and seventh terms

If the common ratio is

q,

then

8q^6=5832

There are six common-ratio steps from the first term

8

to the seventh term

5832.

Thus

q^6=\frac{5832}{8}=729=3^6,

so the positive common ratio is

q=3.

The fifth term is

8q^4=8\cdot3^4=648.

Thus, the correct answer is A.

Problem 5 in other years