$(a)\;AP\qquad(b)\;HP\qquad(c)\;GP\qquad(d)\;None\;of\;the\;above$

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Answer : (b) HP

Explanation : Given that a,b,c are in HP

Therefore 1/a,1/b,1/c are in AP

Multiplying by (a+b+c),

(a+b+c)/a(a+b+c)/b,(a+b+c)/c are in AP

Reducing further

1+(b+c)/a,1+(a+c)/b,1+(a+b)/c are in AP

Minus 1 from each term,

(b+c)/a,(a+c)/b,(a+b)/c are in AP

Therefore, the reciprocals are in HP

a/(b+c),b/(a+c),c/(a+b) are in HP.

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