Home
Class 11
MATHS
Sum of the first p, q and r terms of an ...

Sum of the first p, q and r terms of an A.P are a, b and c, respectively.Prove that `a/p(q-r)+b/q(r-p)+c/r(p-q)=0`

Text Solution

AI Generated Solution

To prove the equation \( \frac{a}{p(q-r)} + \frac{b}{q(r-p)} + \frac{c}{r(p-q)} = 0 \), we start by recalling the formula for the sum of the first \( n \) terms of an arithmetic progression (A.P.). ### Step 1: Write the formula for the sum of the first \( n \) terms of an A.P. The sum of the first \( n \) terms of an A.P. is given by: \[ S_n = \frac{n}{2} \left(2a + (n-1)d\right) \] where \( a \) is the first term and \( d \) is the common difference. ...
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    NCERT|Exercise EXERCISE 9.3|32 Videos
  • SEQUENCES AND SERIES

    NCERT|Exercise EXERCISE 9.1|14 Videos
  • SEQUENCES AND SERIES

    NCERT|Exercise EXERCISE 9.4|10 Videos
  • RELATIONS AND FUNCTIONS

    NCERT|Exercise EXERCISE 2.3|5 Videos
  • SETS

    NCERT|Exercise EXERCISE 1.5|7 Videos

Similar Questions

Explore conceptually related problems

If the pth, qth and rth terms of a G.P. are a,b and c, respectively. Prove that a^(q-r)b^(r-p)c^(p-q)=1 .

The sum of the first p,q,r terms of an A.P.are a,b,c respectively.Show that (a)/(p)(q-r)+(b)/(q)(r-p)+(c)/(r)(p-q)=0

Knowledge Check

  • The p^(th),q^(th) and r^(th) terms of an AP are a,b and c, respectively. The value of a(q-r)+b(r-p)+c(p-q) is

    A
    1
    B
    `-1`
    C
    0
    D
    `1//2`
  • If the pth, qth and rth terms of an A.P. are a,b,c respectively , then the value of a(q-r) + b(r-p) + c(p-q) is :

    A
    0
    B
    1
    C
    abc
    D
    pqr
  • Similar Questions

    Explore conceptually related problems

    The pth, qth and rth terms of an A.P. are a, b and c respectively. Show that a(q – r) + b(r-p) + c(p – q) = 0

    If the p^(t h) ,q^(t h) and r^(t h) terms of a GP are a, b and c, respectively. Prove that a^(q-r)""b^(r-p)""c^(p-q)=1 .

    The sum of the first p,q, rterms of an A.P are a,b, crespectively.Show that (a)/(p)[q-r]+(b)/(q)[r-p]+(c)/(r)[p-q]=0

    If pth,qth and rth terms of an A.P.are a,b,c respectively,then show that (i) a(q-r) +b(r- p) +c(p-q)=0

    If the pth, qth and rth terms of a G.P.are a,b,c respectively,prove that: a^((q-r))C()b^((r-p))dot c^((p-q))=1

    The p^(th),q^(th) and terms of an A.P.are a,b,c,respectively.Show that quad (q-r)a+(r-p)b+(p-q)c=0