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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class11  >>  Sequence and Series
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If a, b and c are in H.P, then a/(b+c), b/(c+a), c/(a+b) are in

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

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1 Answer

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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.
answered Jan 17, 2014 by yamini.v
 

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