Questions

• Arithmetic and Geometric Sequences and Their Summations Understand the concept and the properties of arithmetic sequences Understand the general term of an arithmetic sequence

  已知 $\mathrm{T}(n)$ 為一等差數列的第 $n$ 項。設 $x_{1} 、 y_{1}$ 及 $z_{1}$ 分別為 $\{\mathrm{T}(1), \mathrm{T}(2), \mathrm{T}(3), \ldots, \mathrm{T}(49)\}$這組數的中位數、分佈域及方差, 而 $x_{2} 、 y_{2}$ 及 $z_{2}$ 分別為 $\{\mathrm{T}(51), \mathrm{T}(52), \mathrm{T}(53), \ldots, \mathrm{T}(99)\}$這組數的中位數、分佈域及方差。下列何者必為正確? I. $x_{1}<x_{2}$ II. $y_{1}=y_{2}$ III. $z_{1}>z_{2}$

  2021

• Arithmetic and Geometric Sequences and Their Summations Understand the concept and the properties of arithmetic sequences Understand the general term of an arithmetic sequence

  圖中，第 $1$ 個圖案包含 $8$ 粒點子。對任意正整數 $n$，第 $(n+1)$ 個圖案是由第 $n$ 個圖案加上 $(2n+6)$ 粒點子所組成。求第 $7$ 個圖案的點子數目。

  

  2022

• Arithmetic and Geometric Sequences and Their Summations Understand the concept and the properties of geometric sequences Understand the general term of a geometric sequence

  設 $a_{n}$ 為一等比數列的第 $n$ 項。已知 $a_{1}=8 p^{2} 、 a_{2}=1$ 及 $a_{3}=27 p$, 其中 $p$ 為一實數。求 $a_{4}$ 。

  2022

• Arithmetic and Geometric Sequences and Their Summations Understand the concept and the properties of arithmetic sequences Understand the general term of an arithmetic sequence

  表示一個模式，第1個模式由4個點組成。已知對於任何正整數$n$，第$(n+1)$個模式是通過向第$n$個模式添加$2n$個點形成的。求第8個模式中的點數。

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• Arithmetic and Geometric Sequences and Their Summations Understand the concept and the properties of arithmetic sequences Understand the general term of an arithmetic sequence

  數列的第 $n$ 項是 $10-\frac{n}{3}$。以下哪些是正確的？ I. 數列是一個等差數列。 II. 數列有30個正項。 III. 前50項的和是75。

  2024

• Arithmetic and Geometric Sequences and Their Summations Understand the general term of a geometric sequence Understand the general formulae of the sum to a finite number of terms of an arithmetic sequence and a geometric sequence and use the formulae to solve related problems

  表示一個模式，第一個模式由2個點組成。第 $(n+1)$ 個模式是通過向第 $n$ 個模式添加 $2^{n+2}$ 個點形成的，對於任何正整數 $n$。找出第8個模式中的點數。

  2024

• Arithmetic and Geometric Sequences and Their Summations Understand the concept and the properties of arithmetic sequences Understand the general term of an arithmetic sequence

  一個凸多邊形的內角形成一個等差數列。如果最小的內角和最大的內角分別是$46^{\circ}$和$170^{\circ}$，找出這個多邊形的邊數。

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• Arithmetic and Geometric Sequences and Their Summations Understand the concept and the properties of geometric sequences Explore the general formulae of the sum to infinity for certain geometric sequences and use the formulae to solve related problems

  設$a_{n}$為等比數列的第$n$項。已知$a_{4}=\frac{1}{12}$且$a_{8}=\frac{4}{243}$。如果該數列的無窮級數和小於$\frac{1}{2}$，則下列哪些是正確的？ I. 數列的第一項是$\frac{9}{32}$。 II. $a_{1}+a_{2}+a_{3}+\ldots+a_{10}<-\frac{1}{10}$。 III. $a_{2}+a_{4}+a_{6}+\ldots=\frac{27}{80}$。

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• Series and Sequence Understand the concept and the properties of arithmetic sequences

  在一個特定的圖案中，第1個圖案由$k$個點組成。對於$n \geq 2$，第$n$個圖案是通過向第$(n-1)$個圖案添加$4(n-1)$個點形成的。假設第9個圖案中的點數為145，則$k=$

  2024

• Arithmetic and Geometric Sequences and Their Summations Understand the concept and the properties of geometric sequences Explore the general formulae of the sum to infinity for certain geometric sequences and use the formulae to solve related problems

  設$a_{n}$為公比為$r$的等比數列的第$n$項。已知$a_{2}>0$且該數列的無窮級數和為-3。下列哪些是正確的？ I. $-1<r<0$ II. $-6<a_{1}<-3$ III. 如果$k$是一個正整數，則$a_{1}+a_{2}+\ldots+a_{2k-1}+a_{2k}>3$。

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