The question **"If pth qth and rth terms of an ap is a b and c respectively prove that aq–r+br–p+cp–q=0"** is taken from class-10 ** chapter is Arithmetic Progressions Mathematics ** English-Medium

NCERT-Book ➧ class-10 ➧ Mathematics ➧ English-Medium ➧ Arithmetic Progressions ➧ Theorem For M And N Term Of Same A.P.

**Question:**

**if p ^{th }, q^{th} and r^{th} terms of an A.P. is a, b and c respectively, prove that : a(q – r) + b(r – p) + c(p – q) = 0 .**

Source:www.questionsbanks.com Last updated: 2022-10-11 21:43:54

**Answer:**

Let the first term of A.P. be A and the common difference is d.

a_{p} = a = A + (p -1)d

a = A + (p -1)d …………. (1)

a_{q} = b = A + (q -1)d

b = A + (q -1)d …………. (2)

a_{r} = c = A + (r -1)d

c = A + (r -1)d …………. (3)

a(q – r) + b(r – p) + c(p –q)

= {A + (p -1)d} (q – r) + { A + (q -1)d} (r –p) + { A + (r -1)d}(p – q)

= A{(q – r) + (r – p) + (p – q)} + d {(p – 1) (q – r) + (q – 1) (r –p) + (r -1)(p – q) }

= A (q – r + r – p + p – q) + d (pq – pr – q + r + qr – pq – r + p + pr – qr – p + q)

= A × 0 + d× 0

= 0 Proved

2 Questions Found on same Topics.

If m times of m^{th} term of an A.P. is equal to n times of n^{th} term of same A.P. Show that (m + n)^{th} term is zero.

^{th }, q^{th} and r^{th} terms of an A.P. is a, b and c respectively, prove that : a(q – r) + b(r – p) + c(p – q) = 0 .

Hey! 8 Questions Found on same Chapter.

For what value of k, 2k-7,k+5 and 3k+2 are the consecutive terms of an A.P?

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^{th }, q^{th} and r^{th} terms of an A.P. is a, b and c respectively, prove that : a(q – r) + b(r – p) + c(p – q) = 0 .

If t_{n} = 2n+1 then find the series (A.P).

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All chapters of NCERT Book as ncert solutions have exercise questions, textual questions and so many addtional questions like short answered questions, long answered questions and very long questions, here we included all types of questions answers format that need for a students and other stock holders like teachers and tutors. If pth qth and rth terms of an ap is a b and c respectively prove that aq–r Br–p Cp–q=0 - Questions Bank is from NCERT Solutions class 10 English-Medium subject Mathematics chapter- Arithmetic Progressions Questions bank

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