Sequences & SerieseasyFree

a,b,c in HP: a/(b+c), b/(c+a), c/(a+b) Progression | JEE

JEE Maths question with a full step-by-step solution.

Question
If a,b,ca, b, c are in H.P., then ab+c, bc+a, ca+b\frac{a}{b+c},\ \frac{b}{c+a},\ \frac{c}{a+b} are in
AA.P.
BH.P.correct
CG.P.
DNone of these
Solution
Step 1: a,b,ca,b,c in H.P. ⇒1a,1b,1c\Rightarrow\dfrac1a,\dfrac1b,\dfrac1c in A.P. Step 2: Multiply this A.P. by (a+b+c)(a+b+c) and subtract 11 from each term:
a+b+ca−1, a+b+cb−1, a+b+cc−1=b+ca, c+ab, a+bc are in A.P.\frac{a+b+c}{a}-1,\ \frac{a+b+c}{b}-1,\ \frac{a+b+c}{c}-1=\frac{b+c}{a},\ \frac{c+a}{b},\ \frac{a+b}{c}\ \text{are in A.P.}
 Step 3: Their reciprocals are therefore in H.P., so ab+c,bc+a,ca+b\dfrac{a}{b+c},\dfrac{b}{c+a},\dfrac{c}{a+b} are in H.P. Correct answer: (2)
Still stuck on this question?Ask your doubt on WhatsApp
Similar questions
Sequences & Series · easy
a, b, c, d are in increasing G.P. If the A.M. between a and b is 6 and the A.M. between c…
Sequences & Series · easy
Let a₁, a₂, … and b₁, b₂, … be arithmetic progressions with a₁=25 , b₁=75 and a(100)+b(10…
Sequences & Series · easy
If S_n=(1)/(1·2·3)+(1)/(2·3·4)+⋯+(1)/(n(n+1)(n+2)) , then 8S_∞ is
Sequences & Series · easy
If the sum to infinity of 1+4x+7x²+10x³+⋯ is (35)/(16) , where |x|<1 , then x equals

Solve more, learn faster

Sign up free to solve more JEE Maths questions and explore doMath — timed drills, mastery sprints, bookmarks, and chapter-wise progress tracking.

Sign up freeExplore doMath