Digital ACT Math Practice Question #1620
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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.
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 \(a_1 (3^2) = 18 \implies 9 a_1 = 18 \implies a_1 = 2\)....
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