b39af80f-3579-43d1-8176-c28fe427801c.html

<h4>Writing Expression from Patterns</h4>
<p>Find the number of dots in Step 5, and write an expression to find \(n\) number of dots.</p>
<p><img height="168" src="https://k12.openstax.org/contents/raise/resources/5f6a3a4e86b3cacc1de7c66c1684973c2869bf42"
    width="468"></p>
<p><strong>Step 1</strong> - Make a table to help you find the pattern. </p>
<table class="os-raise-midsizetable">
  <thead>
    <tr>
      <th scope="col">
        Step number
      </th>
      <th scope="col">
        Number of dots
      </th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td>
        0
      </td>
      <td>
        4
      </td>
    </tr>
    <tr>
      <td>
        1
      </td>
      <td>
        7
      </td>
    </tr>
    <tr>
      <td>
        2
      </td>
      <td>
        10
      </td>
    </tr>
    <tr>
      <td>
        3
      </td>
      <td>
        13
      </td>
    </tr>
  </tbody>
</table>
<br>
<p><strong>Step 2</strong> - Notice that the start has 2 rows and 2 columns, or 4 dots.<br>
  Each step adds a row of 2 dots, plus 1 more dot.<br>
  So, each step adds 3 dots.</p>
<p><strong>Step 3</strong> - Continuing this linear pattern, Step 5 would have 19 dots. </p>
<p><strong>Step 4</strong> - An expression could be \(3n+4\). <br>
  This is a linear expression. </p>
<h4>Try It: Writing Expression from Patterns</h4>
<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">
    <p>Find the number of dots in Step 5, and write an expression to find \(n\) number of dots.</p>
    <p><img height="132"
        src="https://k12.openstax.org/contents/raise/resources/48e390686ad23411dd3af33c33aa761446de1202" width="535">
    </p>
  </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 write an expression from a pattern:</p>
  <table class="os-raise-midsizetable">
    <thead>
      <tr>
        <th scope="col">
          Step
        </th>
        <th scope="col">
          Number of dots
        </th>
      </tr>
    </thead>
    <tbody>
      <tr>
        <td>
          0
        </td>
        <td>
          1
        </td>
      </tr>
      <tr>
        <td>
          1
        </td>
        <td>
          3
        </td>
      </tr>
      <tr>
        <td>
          2
        </td>
        <td>
          9
        </td>
      </tr>
      <tr>
        <td>
          3
        </td>
        <td>
          19
        </td>
      </tr>
    </tbody>
  </table>
  <br>
  <p>Each step has that number of dots squared, then doubled, and then one is added.</p>
  <p>So, Step 5 would have 51 dots.</p>
  <p>The expression would be \(2n^2+1\), where \(n\) is the step number.</p>
  <p>This is a quadratic expression.</p>
</div>