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 [JEE Main 2023, 30 Jan (Shift 2)]

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 [JEE Main 2023, 30 Jan (Shift 2)]

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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 \(\log _b c\) be in G.P. If the …

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Let \(a, b, c&gt;1, a^3, b^3\) and \(c^3\) be in A.P., and \(\log _a b, \log _c a\) and \(\log _b c\) be in G.P. If the …

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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 \(\log _b c\) be in G.P. If the …