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Question

If a, b, c are in AP, then 1b+c,1c+a,1a+b are 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 A AP
a,b,c are in AP 2b=a+c
1c+a1b+c=1a+b1c+a
ba(c+a)(b+c)=cb(a+b)(c+a)
cross multiplying gives
ba=cb 2b=a+c
1b+c,1c+a,1a+b are in AP
Hence, option A.

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