title: Why closed form of this recurrence relation is T(n)=7n-4?
body: <p>I'm studying the book <a href="https://www.wiley.com/en-us/Algorithm+Design+and+Applications-p-9781118335918" rel="nofollow noreferrer">Algorithm Design and Applications</a>, and there is a part I couldn't understand:</p>
  <blockquote>
  <h2>1.1.4 Analyzing Recursive Algorithms</h2>
  <p>[...]
  we can characterize the running time, (), of the <strong>recursiveMax</strong> algorithm as</p>
  <pre><code>() =   3            if  = 1
         ⎨ ( − 1) + 7 otherwise
  </code></pre>
  <p>[...] Ideally, we would like to characterize as recurrence equation like that above in <em><strong>closed form</strong></em>, where no references to the function  appear on the righthand side. For the <strong>recursiveMax</strong> algorithm, it isn't too hard to see that a closed form would be () = 7( − 1) + 3 = 7 − 4.</p>
  </blockquote>
  <p>It said:</p>
  <blockquote>
  <p>it isn't too hard to see that a closed form would be () = 7( − 1) + 3 = 7 − 4.</p>
  </blockquote>
  <p>However, I have no idea how this result came out. Could someone explain this to me?</p>