<p>A sequence \(u_1, u_2, u_3, \ldots\) is defined by</p>
<p style="margin-left: 4rem">\(u_1=a,\)<br>\(u_{r+1}=3u_r+5,  r\geqslant 1,\)</p>
<p>where&nbsp;\(a\) is a constant.</p>
<ol class="abc-list"><li data-list-item-id="imported-item-block-3-item-0" data-list-item-path="imported-item-block-3-item-0"><div class="list-item-paragraph">Find expressions for&nbsp;\(u_2\) and \(u_3\) in terms of \(a\).<span class="inline-marks">[2]</span></div></li><li data-list-item-id="imported-item-block-3-item-1" data-list-item-path="imported-item-block-3-item-1"><div class="list-item-paragraph">It is given that&nbsp;\(\displaystyle\sum_{r=1}^{4}u_r=110\). Find the value of \(a\).<span class="inline-marks">[3]</span></div></li></ol>

A sequence \(u_1, u_2, u_3, \ldots\) is defined by

\(u_1=a,\)
\(u_{r+1}=3u_r+5,  r\geqslant 1,\)

Find expressions for \(u_2\) and \(u_3\) in terms of \(a\).

It is given that \(\displaystyle\sum_{r=1}^{4}u_r=110\). Find the value of \(a\).