The correct option is C HP
Given that, a2a3a1a4=a2+a3a1+a4=3(a2−a3a1−a4)
Now, a2a3a1a4=a2+a3a1+a4
⇒1a1+1a4=1a3+1a2 ....(1)
and a2a3a1a4=3(a2−a3a1−a4)
⇒1a4−1a1=3(1a3−1a2) ....(2)
Adding (1) and (2) and then rearranging, we get
2a3=1a4+1a2 ....(3)
Subtracting (1) and (2) and then rearranging, we get
2a2=1a1+1a3 ....(4)
From (3) and (4), we get
Therefore, a1,a2,a3,a4 are in H.P
Ans: C