A geometric sequence has first term 2 and fourth term 54. What is its third term?

1. Write the fourth term in terms of the first: a_4 = a_1 r^3, so 54 = 2r^3. 2. Divide by 2: r^3 = 27. 3. Take the cube root: r = 3. 4. The third term multiplies the first term by r twice: a_3 = 2 x 3^2 = 18. 5. Option B, 27, is r^3 itself, mistaking the cubed ratio for a term of the sequence. _Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 13 "Sequences, Probability and Counting Theory", section 13.3 GEOMETRIC SEQUENCES_