Lily pads \(1,2,3,\ldots\) lie in a row on a pond. A frog makes a sequence of jumps starting on pad \(1\). From any pad \(k\) the frog jumps to either pad \(k+1\) or pad \(k+2\) chosen randomly with probability \(\tfrac{1}{2}\) and independently of other jumps. The probability that the frog visits pad \(7\) is \(\tfrac{p}{q}\), where \(p\) and \(q\) are relatively prime positive integers. Find \(p+q\).