826bd169-a14f-4da5-b9c0-f557ae1a5439.html

<h4>Finding a Common Ratio</h4>
<h5>Definition of a Geometric Sequence</h5>
<p>A geometric sequence is one in which any term divided by the previous term is a constant. This constant is called the common ratio of the sequence. The common ratio can be found by dividing any term in the sequence by the previous term. If \(a_1\) is the initial term of a geometric sequence and \(r\) is the common ratio, the sequence will be</p>
<p>{\(a_1, a_1\cdot r\), \(a_1\cdot r^2\), \(a_1\cdot r^3\), . . .}</p>
<p>How to:</p>
<p>Given a set of numbers, determine if they represent a geometric sequence.</p>
<ol class="os-raise-noindent">
  <li> Divide each term by the previous term.</li>
  <li>Compare the quotients. If they are the same, a common ratio exists and the sequence is geometric.</li>
</ol>
<p>Example:</p>
<p>Is the sequence geometric? If so, find the common ratio.</p>
<ol class="os-raise-noindent" type="a">
  <li> 1, 2, 4, 8, 16, . . .</li>
  <li> 48, 12, 4, 2, . . .
    <ol class="os-raise-noindent" type="a">
      <li>
        Is a geometric sequence. Each term is multiplied by 2, so 2 is the common ratio.
      </li>
      <li>
        This is not geometric because each term is not multiplied by the same constant. There is not a common ratio.
      </li>
    </ol>
  </li>
</ol>
<h4>Try It: Finding a Common Ratio</h4>
<p>Is the sequence geometric? If so, find the common ratio.</p>
<p>100, 20, 4, \(\frac45\), . . .</p>
<br>
<div class="os-raise-ib-cta" data-button-text="Solution" data-fire-event="Reveal1" data-schema-version="1.0">
  <div class="os-raise-ib-cta-content">
  </div>
  <div class="os-raise-ib-cta-prompt">
    <p>Write down your answer, then select the <strong>solution</strong> button to compare your work.
    </p>
  </div>
</div>
<div class="os-raise-ib-content" data-schema-version="1.0" data-wait-for-event="Reveal1">
  <p>Here is how to determine if the sequence is geometric:</p>
  <p>Each term is \(\frac15\) of the previous term. So, the common ratio is \(\frac15\), and this is a geometric sequence.</p>
</div>