<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">A sequence is such that ${{u}_{1}}=p$ where $p$ is a constant and ${{u}_{n+1}}=2{{u}_{n}}-5$, for $n>0$.</span></div><ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Describe how the sequence behaves when</span></div><div class="list-item-paragraph">(A) $p=7$,</div><div class="list-item-paragraph">(B) $p=5$.</div></li><li><div class="list-item-content"><span class="list-item-text">Find the value of $p$ for which ${{u}_{5}}=101$.</span></div><p style="text-align: right;">[2]</p></li></ol></li><li><div class="list-item-content"><span class="list-item-text">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 $n>0$.</span></div><div class="list-item-paragraph">For this sequence, ${{v}_{4}}=2{{v}_{3}}$.</div><ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Find the value of $b$.</span></div><p style="text-align: right;">[3]</p></li><li><div class="list-item-content"><span class="list-item-text">Find an expression in terms of $a$ for ${{v}_{5}}$.</span></div><p style="text-align: right;">[1]</p></li></ol></li><li><div class="list-item-content"><span class="list-item-text">The sum of the first $n$ terms of a series is ${{n}^{3}}-11{{n}^{2}}+4n$, where $n$ is a positive integer.</span></div><ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Find an expression for the $n$th term of this series, giving your answer in its simplest form.</span></div><p style="text-align: right;">[2]</p></li><li><div class="list-item-content"><span class="list-item-text">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 $m$.</span></div><p style="text-align: right;">[2]</p></li></ol></li></ol>

A sequence is such that ${{u}_{1}}=p$ where $p$ is a constant and ${{u}_{n+1}}=2{{u}_{n}}-5$, for $n>0$.

Find the value of $p$ for which ${{u}_{5}}=101$.

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, ${{v}_{4}}=2{{v}_{3}}$.

Find an expression in terms of $a$ for ${{v}_{5}}$.

The sum of the first $n$ terms of a series is ${{n}^{3}}-11{{n}^{2}}+4n$, where $n$ is a positive integer.

Find an expression for the $n$th term of this series, giving your answer in its simplest form.

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 $m$.

N2020 P2 Q2

N2020 P2 Q2

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