Let a, b, c>1, a^3, b^3 and c^3 be in A.P., and log_a b, log_c a and log_b c be in G.P. If the sum of first 20 terms of an A.P., whose first term is…

Let $\displaystyle a, b, c>1, a^3, b^3$ and $\displaystyle c^3$ be in A.P., and $\displaystyle \log _a b, \log _c a$ and $\displaystyle \log _b c$ be in G.P. If the sum of first $\displaystyle 20$ terms of an A.P., whose first term is $\displaystyle \frac{a+4 b+c}{3}$ and the common difference is $\displaystyle \frac{a-8 b+c}{10}$ is -$\displaystyle 444$ , then $\displaystyle a b c$ is equal to: