Arithmetic & Geometric Sequences
The sequence $1,x,y,z$ is arithmetic. The sequence $1,p,q,z$ is geometric.
Both sequences are strictly increasing and contain only integers, and $z$ is
as small as possible. What is the value of $x+y+z+p+q$?
\[
\textbf{(A)}\ 66 \qquad
\textbf{(B)}\ 91 \qquad
\textbf{(C)}\ 103 \qquad
\textbf{(D)}\ 132 \qquad
\textbf{(E)}\ 149
\]