<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">A sequence is such that&nbsp;\(u_1 = a\) and \(u_{n+1} = bu_n\), for&nbsp;\(n \geq 1\). Both&nbsp;\(a\) and \(b\) are constants.</span></div><ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Explain why the sequence 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&nbsp;\(u_2 = 6\), \(u_1 + u_2 + u_3 = 26\), and the sum to infinity exists, find the values of \(a\) and \(b\).</span><span class="inline-marks">[4]</span></div></li></ol></li><li><div class="list-item-paragraph">It is given that&nbsp;\(\sum_{r=1}^{n} r^2 = \frac{1}{6}n(n+1)(2n+1).\)</div><ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Find \(\sum_{r=1}^{n} r(r+2)\) in terms of \(n\). Leave your answer in factorised form.</span><span class="inline-marks">[2]</span></div></li><li><div class="list-item-content"><span class="list-item-text">Hence find \(\sum_{r=2}^{n} (r+1)(r+3)\) in terms of \(n\). You do not need to leave your answer in factorised form.</span><span class="inline-marks">[3]</span></div></li></ol></li></ol>

A sequence is such that \(u_1 = a\) and \(u_{n+1} = bu_n\), for \(n \geq 1\). Both \(a\) and \(b\) are constants.

Explain why the sequence is a geometric progression.

Given that \(u_2 = 6\), \(u_1 + u_2 + u_3 = 26\), and the sum to infinity exists, find the values of \(a\) and \(b\).

It is given that \[\n\sum_{r=1}^{n} r^2 = \frac{1}{6}n(n+1)(2n+1).\n\]

It is given that \(\sum_{r=1}^{n} r^2 = \frac{1}{6}n(n+1)(2n+1).\)

Find \(\sum_{r=1}^{n} r(r+2)\) in terms of \(n\). Leave your answer in factorised form.

Hence find \(\sum_{r=2}^{n} (r+1)(r+3)\) in terms of \(n\). You do not need to leave your answer in factorised form.

2025 YIJC P2 Q4

2025 YIJC P2 Q4