`a`, `b`, `c` are positive integers formaing an incresing `G.P.` and `b-a` is a perfect cube and `log_(6)a+log_(6)b+log_(6)c=6`, then `a+b+c=`
A
`100`
B
`111`
C
`122`
D
`189`
Text Solution
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The correct Answer is:
D
`(d)` `log_(6)(abc)=6` `implies(abc)=6^(6)` Let `a=(b)/(r )` and `c=br` ,brgt `impliesb=36` and `a=(36)/(r )impliesr=2,3,4,6,9,12,18` Also `36(1-(1)/(r ))` is a perfect cube. `impliesr=4` `impliesa+b+c=9+36+144=189`
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