Just an A.P.

Algebra Level 2

$a{ b }^{ 2 }{ c }^{ 3 },{ a }^{ 2 }{ b }^{ 3 }{ c }^{ 4 },{ a }^{ 3 }{ b }^{ 4 }{ c }^{ 5 }$ are in A.P find the least value of a+b+c (where a,b,c are real and positive numbers)