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Problem 559

AMC 12 late, AIME early

Algebra Difficulty 5.0 Find the answer

2. Determine the fourth and fifth terms of the sequence $\frac{8}{3}, \frac{4}{9}, \frac{2}{27}, \ldots$ .

Your answer

Official solution

2. The next term of the sequence is obtained by dividing the numerator of the previous term by 2 and multiplying the denominator by 3.

2 POINTS

The fourth term of the sequence is $\frac{2: 2}{27 \cdot 3}=\frac{1}{81}$ .

2 POINTS

The fifth term of the sequence is $\frac{1: 2}{81 \cdot 3}=\frac{\frac{1}{2}}{243}=\frac{1}{486}$

2 POINTS

TOTAL 6 POINTS

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.