Show that x(q-r) + y(r-p) + z(p-q) = 0, Mathematics

Assignment Help:

If the pth, qth & rth term of an AP is x, y and z respectively, show that x(q-r) + y(r-p) + z(p-q) = 0

Ans:    pth term ⇒ x = A + (p-1) D

qth term ⇒ y = A + (q-1) D

rth term ⇒ z = A + (r-1) D

T.P x(q-r) + y(r-p) + z(p-q) = 0

={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)

+ (r-1) (r-p) + (r-1) (p-q)}

⇒ A.0 + D{p(q-r) + q(r-p) + r (p-q)

- (q-r) - (r-p)-(p-q)}

= A.0 + D.0 = 0.

Hence proved

 


Related Discussions:- Show that x(q-r) + y(r-p) + z(p-q) = 0

Siquence aned series, if 4,a and 16 are in the geometric sequence. Find the...

if 4,a and 16 are in the geometric sequence. Find the value

Symmetric and anti-symmetric relation on a set, 1. Let A = {1,2, 3,..., n} ...

1. Let A = {1,2, 3,..., n} (a) How many relations on A are both symmetric and anti-symmetric? (b) If R is a relation on A that is anti-symmetric, what is the maximum number o

.probability, a box contains 4 white and 6 green balls.Two balls are drawn ...

a box contains 4 white and 6 green balls.Two balls are drawn randomly with replacement.Show the probability on tree dig.

Calculate the height of the tunnel and the perimeter, The adjoining figure...

The adjoining figure shows the cross-section of a railway tunnel. The radius of the tunnel is 3.5m (i.e., OA=3.5m) and ∠AOB=90 o . Calculate : i.       the height of the

MARKOV PROCESS, EXPLAIN HOW MARKOV PROCESS IS APPLIED IN BRAND SWITCHING?

EXPLAIN HOW MARKOV PROCESS IS APPLIED IN BRAND SWITCHING?

Quartic polynomial, Question: Let f be a quartic polynomial (ie. a poly...

Question: Let f be a quartic polynomial (ie. a polynomial of degree 4). Suppose that f has zeros at -2; 1; 3; 4 and that f(0) = 4. Sketch a graph of f. If f(x) is

Bar charts, I''m supposed to be writing a critique for my maths project whe...

I''m supposed to be writing a critique for my maths project where i compare the prices for different holidays. i don''t know what to write for a critique though, any tips on what w

Order of Operations with Fractions, 1.)3 3/8 divided by 4 7/8 plus 3 2.)4 ...

1.)3 3/8 divided by 4 7/8 plus 3 2.)4 1/2 minus 3/4 divided by 2 3/8

Find out the value of n element of a set, A set consists of (2n+1) elements...

A set consists of (2n+1) elements. If the number of subsets of this set which consist of at most n elements is 8192. Find out the value of n. Ans: The following set has (2n + 1

Calculus, application of radious of curvatur

application of radious of curvatur

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd