Let $ a, b, c1, 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 $ \frac{a+4 b+c}{3} $ and the common difference is $ \frac{a-8 b+c}{10} $ is $ -444 $, then $ a b c $ is equal to

Question

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 $ \frac{a+4 b+c}{3} $ and the common difference is $ \frac{a-8 b+c}{10} $ is $ -444 $, then $ a b c $ is equal to

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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 _{…

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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 _{…