ACT Math Practice Question #1282 (Hard (33)) | Test Citadel
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ACT Math Difficulty: Hard (33)

Digital ACT Math Practice Question #1282

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In a geometric sequence of positive real numbers, the third term is $18$ and the sixth term is $486$. What is the first term of this sequence?
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Ratio $a_6 / a_3 = 486 / 18 = 27 = 3^3 \implies r = 3$. Step backwards: $a_2 = 18 / 3 = 6$, $a_1 = 6 / 3 = 2$. Under 10 seconds.

Masterclass Solution & Distractor Trap Analysis

In a geometric sequence, $a_n = a_1 r^{n-1}$. Given $a_3 = a_1 r^2 = 18$ and $a_6 = a_1 r^5 = 486$. Dividing the two equations: $\frac{a_6}{a_3} = \frac{a_1 r^5}{a_1 r^2} = r^3 = \frac{486}{18} = 27$. Since $r^3 = 27$, the common ratio is $...

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

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