title: Iterative recurrence... Iteration method
body: <p>I have tried to solve the following recurrence relation using Iteration method,</p>
  
  <pre><code>T(1) = 8  
  T(n) = 3T(n-1) - 15
  </code></pre>
  
  <p>Iterations:</p>
  
  <p><strong>i=1</strong>  </p>
  
  <pre><code>T(n) = 3(3T(n-2) - 15) -15
  </code></pre>
  
  <p><strong>i=2</strong>  </p>
  
  <pre><code>3(3(3T(n-3) - 15) -15) - 15
  </code></pre>
  
  <p><strong>i=3</strong>  </p>
  
  <pre><code> 3(3(3(3T(n-4) - 15) -15) - 15) - 15
  </code></pre>
  
  <p><strong>i=4</strong> </p>
  
  <pre><code>3(3(3(3(3T(n-5) - 15) -15) - 15) - 15) - 15
  </code></pre>
  
  <p>From the iteration pattern I found that<br>
  <strong>T(n) = 3<sup>(i+1)</sup> * T(n-(i+1)) - 15</strong></p>
  
  <p>Now I need to find the summation for this recurrence relation and obtain the closed form. I'm just not sure how to proceed.</p>
  
  <p>Can someone guide me to solving this problem? </p>