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

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

 

Posted Date: 4/8/2013 5:17:52 AM | Location : United States







Related Discussions:- Show that x(q-r) + y(r-p) + z(p-q) = 0, Assignment Help, Ask Question on Show that x(q-r) + y(r-p) + z(p-q) = 0, Get Answer, Expert's Help, Show that x(q-r) + y(r-p) + z(p-q) = 0 Discussions

Write discussion on Show that x(q-r) + y(r-p) + z(p-q) = 0
Your posts are moderated
Related Questions
Class limits These are numerical values, which limits uq extended of a given class that is all the observations in a provided class are expected to fall in the interval which

Let E; F be 2 points in the plane, EF has length 1, and let N be a continuous curve from E to F. A chord of N is a straight line joining 2 points on N. Prove if 0 and N has no cho

whats nine plus 10

sin10+sin20+sin30+....+sin360=0 sin10+sin20+sin30+sin40+...sin180+sin(360-170)+......+sin(360-40)+sin(360-30)+sin(360-20)+sin360-10)+sin360 sin360-x=-sinx hence all terms cancel

The curve (y+1) 2 =x 2 passes by the points (1, 0) and (- 1, 0). Does Rolle's Theorem clarify the conclusion that  dy dx  vanishes for some value of x in the interval -1≤x≤1?

The probability of a rare disease striking a described population is 0.003. A sample of 10000 was examined. Determine the expected no. suffering from the disease and thus find out

a. Estimate the following model,  C t   =  β 0   +  β 1 * DI t +  ε t             Where C t = Aggregate Consumption Expenditure in Australia, quarterly data for the per

Q. Adding Fractions with the Same Denominator? Adding fractions with the same denominator is easy- you add the numerators (the tops), and you leave the denominator alone!

what is classification and how can you teach it?

Describe some Example of substitution method of Linear Equations with solution.