If three positive real numbers a,b,c are in A.P. such that abc=4, then the minimum possible value of b is

Let d be the common difference of the A.P., then             4=abc=(b−d)b(b+d)=bb2−d2⇒        b3=4+bd2≥4 ∵b>0,d2≥0⇒    b≥22/3                Thus, minimum possible value of b is 22/3, that is the case when d=0.