Question 2
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 $\frac{1}{2}$ and independently of other jumps. The probability that the frog visits pad $7$ is $\frac{p}{q},$ where $p$ and $q$ are relatively prime positive integers. Find $p + q.$