ACT Math Practice Question #1212 (Hard (35)) | Test Citadel
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ACT Math Difficulty: Hard (35)

Digital ACT Math Practice Question #1212

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What is the sum of the infinite geometric series $18 - 12 + 8 - \frac{16}{3} + \cdots$?
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$S = a / (1 - r) = 18 / (1 - (-2/3)) = 18 / (5/3) = 54/5$.

Masterclass Solution & Distractor Trap Analysis

The first term is $a_1 = 18$. The common ratio is $r = \frac{-12}{18} = -\frac{2}{3}$. Since $|r| = |-\frac{2}{3}| = \frac{2}{3} < 1$, the infinite geometric series converges. The sum formula is: $$S_\infty = \frac{a_1}{1 - r} = \frac{18}{1...

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

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