<p>A company posted a video on a social media platform to advertise a new product. The video is uploaded at the start of \(1\)st April and the number of daily views is recorded at the end of each day. Let \(u_n\), where \(n \geq 1\), denotes the number of daily views recorded each day. It is given that</p>
<p style="text-align: center">\[u_{n+1} = (1+k)u_n,\]</p>
<p>where \(k\) is a positive constant.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Explain why the sequence \(\{u_n\}\) is a geometric progression.</span><span class="inline-marks">[1]</span></div></li><li><div class="list-item-content"><span class="list-item-text">Given that the number of daily views recorded at the end of \(1\)st April is \(311\) and the total number of daily views recorded from \(1\)st April to \(3\)rd April is \(4043\). Find the value of \(k\).</span><span class="inline-marks">[3]</span></div></li><li><div class="list-item-content"><span class="list-item-text">Explain why there is no limit to the total number of daily views in the long run.</span><span class="inline-marks">[1]</span></div></li></ol>
<p>The company also looks at the number of comments being posted on the social media platform. The number of daily comments is recorded at the end of each day. It is given that \(v_r\), where \(r \geq 1\), denotes the number of daily comments recorded and it is defined by the following relation:</p>
<p style="text-align: center">\[v_r = \begin{cases} u_r & \text{for } 1 \leq r \leq 4, \\ v_{r-1} + 80 & \text{for } r \geq 5. \end{cases}\]</p>
<ol class="abc-list" start="4"><li><div class="list-item-content"><span class="list-item-text">Show that the total number of comments up to the \(r\)th day, where \(r \geq 5\), is \(40r^2 + 8117r - t\), where \(t\) is a constant to be determined.</span><span class="inline-marks">[3]</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find the least number of days required for the total number of daily comments to exceed \(100\) \(000\).</span><span class="inline-marks">[3]</span></div></li></ol>

A company posted a video on a social media platform to advertise a new product. The video is uploaded at the start of \(1\)st April and the number of daily views is recorded at the end of each day. Let \(u_n\), where \(n \geq 1\), denotes the number of daily views recorded each day. It is given that

Explain why the sequence \(\{u_n\}\) is a geometric progression.

Given that the number of daily views recorded at the end of \(1\)st April is \(311\) and the total number of daily views recorded from \(1\)st April to \(3\)rd April is \(4043\). Find the value of \(k\).

Explain why there is no limit to the total number of daily views in the long run.

The company also looks at the number of comments being posted on the social media platform. The number of daily comments is recorded at the end of each day. It is given that \(v_r\), where \(r \geq 1\), denotes the number of daily comments recorded and it is defined by the following relation:

\[v_r = \begin{cases} u_r & \text{for } 1 \leq r \leq 4, \\ v_{r-1} + 80 & \text{for } r \geq 5. \end{cases}\]

Show that the total number of comments up to the \(r\)th day, where \(r \geq 5\), is \(40r^2 + 8117r - t\), where \(t\) is a constant to be determined.

Find the least number of days required for the total number of daily comments to exceed \(100\) \(000\).

2025 JPJC P1 Q11

2025 JPJC P1 Q11