These Ten-Year-Series (TYS) worked solutions with video explanations for 2020 A Level H2 Mathematics Paper 2 Question 2 are suggested by Mr Gan. For any comments or suggestions please contact us at support@timganmath.edu.sg.
2020 A Level H2 Math Paper 2 Question 2
(a)
A sequence is such that ${{u}_{1}}=p$ where $p$ is a constant and ${{u}_{n+1}}=2{{u}_{n}}-5$, for $n>0$.
(a) A sequence is such that ${{u}_{1}}=p$ where $p$ is a constant and ${{u}_{n+1}}=2{{u}_{n}}-5$, for $n>0$.
(i) Describe how the sequence behaves when
(A) $p=7$,
[1]
(B) $p=5$.
[1]
(i) Describe how the sequence behaves when
(A) $p=7$,
[1]
(B) $p=5$.
[1]
(ii) Find the value of $p$ for which ${{u}_{5}}=101$.
[2]
(ii) Find the value of $p$ for which ${{u}_{5}}=101$.
[2]
(b)
Another sequence is defined by ${{v}_{1}}=a$, ${{v}_{2}}=b$, where $a$ and $b$ are constants, and ${{v}_{n+2}}={{v}_{n}}+2{{v}_{n+1}}-7$, for $n>0$.
(b) Another sequence is defined by ${{v}_{1}}=a$, ${{v}_{2}}=b$, where $a$ and $b$ are constants, and ${{v}_{n+2}}={{v}_{n}}+2{{v}_{n+1}}-7$, for $n>0$.
For this sequence, ${{v}_{4}}=2{{v}_{3}}$.
(i) Find the value of $b$.
[3]
For this sequence, ${{v}_{4}}=2{{v}_{3}}$.
(i) Find the value of $b$.
[3]
(ii) Find an expression in terms of $a$ for ${{v}_{5}}$.
[1]
(ii) Find an expression in terms of $a$ for ${{v}_{5}}$.
[1]
(c)
The sum of the first $n$ terms of a series is ${{n}^{3}}-11{{n}^{2}}+4n$, where $n$ is a positive integer.
(c) The sum of the first $n$ terms of a series is ${{n}^{3}}-11{{n}^{2}}+4n$, where $n$ is a positive integer.
(i) Find an expression for the $n$th term of this series, giving your answer in its simplest form.
[2]
(i) Find an expression for the $n$th term of this series, giving your answer in its simplest form.
[2]
(ii) The sum of the first $m$ terms of this series, where $m>3$, is equal to the sum of the first three terms of this series. Find the value of $m$.
[2]
(ii) The sum of the first $m$ terms of this series, where $m>3$, is equal to the sum of the first three terms of this series. Find the value of $m$.
[2]
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