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A geometric sequence has first term 2 and fourth term 54. What is its third term?
A18
B27
C12
D36
Answer & Solution
Correct answer: A. 18
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_
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