If each term of a geometric progression ${\mathrm{a}}_1,{\mathrm{a}}_2,{\mathrm{a}}_3,\dots$ with ${\mathrm{a}}_1=\frac{1}{8}$ and ${\mathrm{a}}_2\ne {\mathrm{a}}_1$, is the arithmetic mean of the next two terms and ${\mathrm{S}}_{\mathrm{n}}={\mathrm{a}}_1+{\mathrm{a}}_2+\dots +{\mathrm{a}}_{\mathrm{n}}$, then ${\mathrm{S}}_{20}-{\mathrm{S}}_{18}$ is equal to

• A

  $2^{15}$
• B

  $-2^{18}$
• C

  $2^{18}$
• Correct answer
  D

  $-2^{15}$

Hence, the correct answer is option: 'D'.