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Grade 11Algebra

IF a1, a2, ….., an are in HP. Then,
a1/a1+a2+a3....+an , a2/a1+a2+a3....+an , a3/a1+a2+a3....+an , …......., an/a1+a2+a3....+an-1 Are in what?

Profile image of Surya
8 Years agoGrade 11
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1 Answer

Profile image of Arun
ApprovedApproved Tutor Answer8 Years ago
Dear student
 
if 
a1, a2, ….., an            (H.P.)
 
then
 
1/a1, 1/a2,........., 1/an    (A.P.)
 
 
Multiply by (a1 +a2+....an)
 
(a1 +a2+....an) / a1, (a1 +a2+....an)/a2, …................(a1 +a2+....an)/an          (A.P.)
 
hence
 
a1 /(a1 +a2+....an) , a2 / (a1 +a2+....an), ................ , an / (a1 +a2+....an)         will be in H.P.
 
Hence answer of this question will be H.P.
 
 
Regards
Arun (askIITians forum expert)

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