# 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

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 and related topic is Theorem For M And N Term Of Same A.P.. 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 Students need stored questions answers as questions banks which can be used anytime anywhere as we can't learn so many ncert solutions.

## 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

##### Question Origin:

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

if pth , qth and rth 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

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

ap = a =  A + (p -1)d

a = A + (p -1)d    …………. (1)

aq = b = A + (q -1)d

b = A + (q -1)d    …………. (2)

ar = 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

## Chapter: Arithmetic Progressions | Topic: Theorem For M And N Term Of Same A.P.

2 Questions Found on same Topics.

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

if pth , qth and rth terms of an A.P. is a, b and c respectively, prove that : a(q – r) + b(r – p) + c(p – q) = 0 .

### Chapter: Arithmetic Progressions (Mathematics English-Medium)

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?

The sum of n terms of two A.P.’s is in the ratio 3n + 8: 7n + 15. Find the ratio of their 9th terms.

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

Which term will be zero of A.P: 105, 98, 91, ........................ ?

if pth , qth and rth terms of an A.P. is a, b and c respectively, prove that : a(q – r) + b(r – p) + c(p – q) = 0 .

If tn = 2n+1 then find the series (A.P).

Which term of the sequence 114, 109, 104…………is the first negative term?

If the sum of nth term of an A.P. is define as Sn = 3n2 + 4 then find the nth term?

# 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

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## 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

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