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Question

If a1, a2, a3.....an are in H.P., then a1a2+a3+......an . a2a1+a3+.....+an,...... ana1+a2+.......+an1

are in


A

A.P.

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B

G.P.

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C

H.P.

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D

A.G.P

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Solution

The correct option is C

H.P.


a1, a2, a3 ...........an are in H.P. 1a1, 1a2, 1a3................ 1an are in A.P.

Multiply each term by a1 + a2 + a3 .........+ an then substract 1 from each term

We get a2+a3+.........+ana1, a1+a3+.......+ana2, ........... a1+a2+..........+an1an are in A.P.

a1a2+a3+........+an, a2a1+a3+...........+an, ........... ana1+a2+........+an1 are in H.P.


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