ACT Math Practice Question #1620 (Hard (600)) | Test Citadel
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ACT Math Difficulty: Hard (600)

Digital ACT Math Practice Question #1620

Test your problem-solving accuracy on this official-caliber item. Select an answer choice to check your reasoning instantly.

The third term of a geometric sequence is 18 and the sixth term is 486. What is the first term of this sequence?
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Ratio jumps 3 steps from term 3 to 6: 486/18 = 27 -> r=3. Step backwards: 18 -> 6 -> 2. The first term is 2.

Masterclass Solution & Distractor Trap Analysis

In a geometric sequence, \(a_n = a_1 r^{n-1}\). Thus \(a_6 / a_3 = r^3 = \frac{486}{18} = 27\), so \(r = 3\). Since \(a_3 = a_1 r^2 = 18\), we have \(a_1 (3^2) = 18 \implies 9 a_1 = 18 \implies a_1 = 2\)....

Distractor Analysis: Trap choice eliminates careless test-takers who confuse roots with coordinates...

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