A geometric sequence has first term 3 and fourth term 24. What is its second term?

1. The fourth term is the first term multiplied by the common ratio three times, so a_4 = 3r^3. 2. Substituting the known value gives 24 = 3r^3. 3. Dividing both sides by 3 gives r^3 = 8. 4. Taking the cube root gives r = 2. 5. The second term is the first term multiplied by the ratio once: 3 times 2 = 6. 6. Dividing 24 by 3 and stopping would give 8, which mistakes the ratio cubed for the second term. 7. The value 12 is the third term, since 3 times 2 times 2 = 12, so one multiplication too many lands there. _Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 13 "Sequences, Probability and Counting Theory", section 13.3 Geometric Sequences_