<p>There is a standard way to induce an arithmetic progression out of a given geometric progression, as illustrated from the following examination question.</p>
<p>The geometric sequence \(u_1, u_2, u_3, \dots\) has common ratio \(r\).</p>
<p>Consider the sequence \(A = \{a_n = \log_2 |u_n| : n \in \mathbb{Z}^+\}\).</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Show that&nbsp;\(A\) is an arithmetic sequence, stating its common difference \(d\) in terms of \(r\).</span></div></li></ol>
<p>A particular geometric sequence has&nbsp;\(u_1 = 3\) and a sum to infinity of \(4\).</p>
<ol class="abc-list" start="2"><li><div class="list-item-content"><span class="list-item-text">Find the value of \(d\).</span></div></li></ol>

There is a standard way to induce an arithmetic progression out of a given geometric progression, as illustrated from the following examination question.

The geometric sequence \(u_1, u_2, u_3, \dots\) has common ratio \(r\).

Consider the sequence \(A = \{a_n = \log_2 |u_n| : n \in \mathbb{Z}^+\}\).

Show that \(A\) is an arithmetic sequence, stating its common difference \(d\) in terms of \(r\).

Connecting GP with AP and Summation

Connecting GP with AP and Summation