Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
BITSAT2011MathematicsSequences and SeriesActual

If ( p ^ th , q ^ th ) and ( r ^ th ) terms of H.P. are ( u , v , w ) respectively, then find the value of the expression ((q-r) v w+(r-p) w u+(p-q) u v ).

Options

  1. A2
  2. B0
  3. C4
  4. D8

Correct answer

B. 0

Step-by-step solution

Let H.P. be ( 1 a + 1 a + d + 1 a +2 ~d + ) ( aligned & u = 1 a +( p -1) d , v = 1 a +( q -1) d , & w = 1 a +( r -1) d a +( p -1) d = 1 u & a +( q -1) d = 1 v , a +( r -1) d = 1 w & ( q - r ) a +( p -1) d +( r - p ) a +( q -1) d + & = 1 u ( q - r )+ 1 v ( r - p )+ . (q-r) vw + . . = 0 aligned )

Practice Sequences and Series on Quantrex Academy →

More from Sequences and Series

If a 0, b 0, c 0 and a, b, c are distinct, then (a+b)(b+c)(c+a) is greater than 2024If _ k=1 ^n k(k+1)(k-1)=p n^4+q n^3+t n^2+s n where p, q, t and s are constants, then the value of s is equal to 2024There are four numbers of which the first three are in GP and the last three are in AP, whose common difference is 6 . If the first and the last numbers are equal, then two other n 2024If A=1+r^a+r^ 2 a +r^ 3 a + and B =1+ r ^ b + r ^ 2 ~b + r ^ 3 ~b + , then a b is equal to 2024The sum of the infinite series 1+ 5 6 + 12 6^2 + 22 6^3 + 35 6^4 + 51 6^5 + 70 6^6 + . . is equal to: 2024If ⁻¹ [ 1 1+1.2 ]+ ⁻¹ [ 1 1+2.3 ]+ + ⁻¹ [ 1 1+n(n+1) ]= ⁻¹[x] , then x is equal to 2024If arithmetic mean of two distinct positive real number a and b(a b) be twice their geometric mean, then a: b= 2024If y= ⁻¹ 1 x^2+x+1 + ⁻¹ 1 x^2+3 x+3 + ⁻¹ 1 x^2+5 x+7 + .to n terms, then d y d x = 2024 Full Sequences and Series list All BITSAT PYQs