Here is the recursive definition, for reference
\(T(1) = 5 \)\( T(n) = 3 T(n/2) + 7\) for \(n \ge 2\)
First, substitute the recursive part of the definition into itself and guess the pattern to get the result after k substitutions.
\( \begin{eqnarray*} T(n) &=& 3\cdot T(n/2) + 7 \\ &=& 3(3\cdot T(n/4) + 7) + 7 \\ &=& 3(3(3\cdot T(n/8) + 7) + 7) + 7 \end{eqnarray*} \)
Find and fix any errors in the above, then return to the hints page for help with the rest of the calculation.