If a,b,care in A.P as well as in G.P. then
a=b≠c
a≠b=c
a≠b≠c
a=b=c
Explanation for the correct option:
Finding the value:
Since, a,b,c are in Arithmetic Progression.
Therefore, b=a+c2
Squaring, b2=(a+c)24...(i)
Also, a,b,c are in Geometric Progression
Therefore, b2=ac....(ii)
Equating (i)&(ii)
(a+c)24=ac⇒a2+c2+2ac=4ac⇒(a2+c2-2ac)=0⇒(a-c)=0⇒a=c
Put ain (ii), b=c
Therefore, a=b=c
Hence, correct option is (D).