If each term of a geometric progression $\mathrm { a } _ { 1 } , \mathrm { a } _ { 2 } , \mathrm { a } _ { 3 } , \ldots$ with $\mathrm { a } _ { 1 } = \frac { 1 } { 8 }$ and $\mathrm { a } _ { 2 } \neq \mathrm { a } _ { 1 }$, is the arithmetic mean of the next two terms and $\mathrm { S } _ { \mathrm { n } } = \mathrm { a } _ { 1 } + \mathrm { a } _ { 2 } + \ldots + \mathrm { a } _ { \mathrm { n } }$, then $\mathrm { S } _ { 20 } - \mathrm { S } _ { 18 }$ is equal to\\
(1) $2 ^ { 15 }$\\
(2) $- 2 ^ { 18 }$\\
(3) $2 ^ { 18 }$\\
(4) $- 2 ^ { 15 }$