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A streaming service had 6,000 subscribers at the end of its first month of operation, and the number of subscribers tripled in each month after that. At the end of which month did the service first have 1,458,000 subscribers?
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Correct answer
C
Method (geometric-sequence term formula): the subscriber counts form a geometric sequence with first term a(1) = 6,000 and common ratio r = 3. The count at the end of month n is a(n) = 6,000 × 3⁽ⁿ⁻¹⁾. Note the exponent is (n − 1), not n: at the end of month 1 the exponent is 0, so a(1) = 6,000 × 1 = 6,000, which matches the given starting count.
Set a(n) = 1,458,000: divide both sides by 6,000 to get 3⁽ⁿ⁻¹⁾ = 1,458,000 ÷ 6,000 = 243. Since 243 = 3 × 3 × 3 × 3 × 3 = 3⁵, the exponent (n − 1) = 5, so n = 6. The service first reaches 1,458,000 subscribers at the end of the 6th month. Answer: (C).
Method (direct listing, fastest check): write the monthly counts and stop when you hit the target. Month 1: 6,000. Month 2: 18,000. Month 3: 54,000. Month 4: 162,000. Month 5: 486,000. Month 6: 1,458,000. Counting the listed terms, 1,458,000 is the 6th value, confirming the 6th month.
The reliable safeguard is that the term number is always one more than how many times the ratio has been applied.
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