Home
Class 11
MATHS
The p^(t h),q^(t h)and r^(t h)terms of ...

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

Text Solution

AI Generated Solution

To solve the problem, we need to show that \((q - r)a + (r - p)b + (p - q)c = 0\) given that the \(p^{th}\), \(q^{th}\), and \(r^{th}\) terms of an arithmetic progression (A.P.) are \(a\), \(b\), and \(c\) respectively. ### Step-by-Step Solution: 1. **Understanding the A.P. Terms**: The \(n^{th}\) term of an A.P. can be expressed as: \[ A_n = A_1 + (n - 1)d ...
Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    NCERT ENGLISH|Exercise SOLVED EXAMPLES|24 Videos

  • SEQUENCES AND SERIES

    NCERT ENGLISH|Exercise EXERCISE 9.2|18 Videos

  • RELATIONS AND FUNCTIONS

    NCERT ENGLISH|Exercise EXERCISE 2.3|5 Videos

  • SETS

    NCERT ENGLISH|Exercise EXERCISE 1.5|7 Videos

Similar Questions

Explore conceptually related problems

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 .

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 .

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

The 5^(t h) , 8^(t h) and 11^(t h) terms of a G.P. are p, q and s, respectively. Show that q^2=p s .

If a ,b ,c are respectively the p^(t h),q^(t h)a n dr^(t h) terms of a G.P. show that (q-r)loga+(r-p)logb+(p-q)logc=0.

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

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

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

If pth, qth, and rth terms of an A.P. are a ,b ,c , respectively, then show that (1) a(q-r)+b(r-p)+c(p-q)=0 (2)(a-b)r+(b-c)p+(c-a)q=0

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