Question

Let ( a, b, c b a, a r, a v^{2} )
aso ( _{1} frac{a+b+c}{3}=b+2 )
( Rightarrow quad a+a r+a x^{2}=39 r+6 )
( Rightarrow quad a r^{2}-2 a r+a=6 )
( Rightarrow quad a(r+)^{2}=frac{6}{9} )
( Rightarrow quad frac{6}{9} ) must ( b e ) a perfect oquare
[
begin{aligned} &=(r+1)^{2} text { is be } end{aligned}
]
3) ( a=6 ).
( gamma-1=pm 1 )
( r=0,2,0 ) (mat possible)
( therefore quad a^{2}+a-14 )
( operatorname{ajv} e^{frac{36+6-14}{7}}=4 ) thes
nating solved by am ition

# Let a,b,c be positive integers such that is an integer. If a,b,c are in geometric progression and a' + a -14 5) the arithmetic mean of a,b,c is b + 2, then the value of 4 * is (JEE(Advanced)-2014, 3] a +1 ADI CAL

Solution