taiwan-gsat 2023 Q9

taiwan-gsat · Other · gsat__math-a 5 marks Sequences and series, recurrence and convergence Summation of sequence terms

Let $a_{1}, a_{2}, a_{3}, \ldots, a_{n}$ be a geometric sequence with first term 3 and common ratio $3\sqrt{3}$. Select the number of terms $n$ that satisfy the inequality
$$\log_{3} a_{1} - \log_{3} a_{2} + \log_{3} a_{3} - \log_{3} a_{4} + \ldots + (-1)^{n+1} \log_{3} a_{n} > 18$$
among the possible options.
(1) 23
(2) 24
(3) 25
(4) 26
(5) 27

Let $a_{1}, a_{2}, a_{3}, \ldots, a_{n}$ be a geometric sequence with first term 3 and common ratio $3\sqrt{3}$. Select the number of terms $n$ that satisfy the inequality

$$\log_{3} a_{1} - \log_{3} a_{2} + \log_{3} a_{3} - \log_{3} a_{4} + \ldots + (-1)^{n+1} \log_{3} a_{n} > 18$$

among the possible options.\\
(1) 23\\
(2) 24\\
(3) 25\\
(4) 26\\
(5) 27

Paper Questions

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