If a, b, c are three unequal numbers such tha | vedclass

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(A) Since $a, b, c$ are in $A.P.$,we have $2b = a + c$,which implies $c - b = b - a$. Given that $b - a, c - b, a$ are in $G.P.$,we have $(c - b)^2 =

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$1 : 2 : 3$

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(A) Since $a, b, c$ are in $A.P.$,we have $2b = a + c$,which implies $c - b = b - a$. Given that $b - a, c - b, a$ are in $G.P.$,we have $(c - b)^2 = (b - a)a$. Substituting $c - b = b - a$ into the $G.P.$ condition,we get $(b - a)^2 = (b - a)a$. Since $a, b, c$ are unequal,$b - a 
eq 0$,so we can divide by $(b - a)$ to get $b - a = a$,which means $b = 2a$. Substituting $b = 2a$ into $2b = a + c$,we get $2(2a) = a + c$,so $4a = a + c$,which gives $c = 3a$. Thus,$a : b : c = a : 2a : 3a = 1 : 2 : 3$.

If $a, b, c$ are three unequal numbers such that $a, b, c$ are in $A.P.$ and $b - a, c - b, a$ are in $G.P.$,then $a : b : c$ is

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