Question

12. किसी समांतर श्रेढ़ी के गवें, वें तथा वें पद क्रमशः a, b और © हैं, तो सिद्ध कीजिए कि
a(q-r)+ b(r-p)+ c(p-q) = 0.​

Answer 1

Step-by-step explanation:

let A .P. ., A+(A+d)+(A+2d)+.........

a=1 d=A+d -A=d

pth term= A+(p- 1)d=a..........(1)

qth term = A+(q -1)d=b........(2)

rth term=A+(r -1)d=c.............(3)

substract by (2)and (3).

(q-r)d=b- c......(4)

repeat substract by (3) and (1).

(r-p)d=c-a.....(5)

repeat substract by (1) and (2).

(p-q)d=a-b........(6).

equation (4),(5) and (6) multiply in a,b and c.

=d[(q-r)a+(r-p)b+(p-q)c]=0

divide both side in d.

(q-r)a+(r-p)b+(p-q)c=0

or

a(q-r)+b(r-p)+c(p-q)=0

Hence prove.