# Unrolling Problem 1

Here is the recursive definition, for reference

$$T(1) = 5$$

$$T(n) = 3 T(n/2) + 7$$ for $$n \ge 2$$

### Partial Solution

First, substitute the recursive part of the definition into itself and guess the pattern to get the result after k substitutions.

$$\begin{eqnarray*} T(n) &=& 3\cdot T(n/2) + 7 \\ &=& 3(3\cdot T(n/4) + 7) + 7 \\ &=& 3(3(3\cdot T(n/8) + 7) + 7) + 7 \end{eqnarray*}$$