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Question

If a2a3a1a4=a2+a3a1+a4=3(a2−a3a1−a4) then a1, a2, a3, a4 in:

A
AP
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B
GP
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C
HP
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D
none of these
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Solution

The correct option is C HP
Given that, a2a3a1a4=a2+a3a1+a4=3(a2a3a1a4)
Now, a2a3a1a4=a2+a3a1+a4
1a1+1a4=1a3+1a2 ....(1)
and a2a3a1a4=3(a2a3a1a4)
1a41a1=3(1a31a2) ....(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

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