Let a, b, c>1, a³, b³ and c³ 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 (a+4 b+c)/3 and the common difference is (a-8 b+c)/10 is -444, then a b c is equal to:

Sequence and Series: JEE Main 2023 Mathematics question

JEE Main 2023 · 30 Jan, Evening shift · Q5267

JEE Main 202330 Jan, Evening shiftMathematicsMediumSequence and Series179× since 2002

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}

-444

, then

a b c

is equal to :