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The pth, qth, and rth term of an AP are a, b and c respectively. Show that a(q-r) +b(r-p) +c(p-q) =0.

Posted by Madhav Gautam 7 years, 9 months ago

CBSE > Class 10 > Mathematics

3 answers

Namrata Nath 7 years, 9 months ago

Let A =first term of the ap Let d =common difference of the ap Now a=A+(p-1)d............1 b=A+(q-1)d............2 c=A+(r-1)d.............3 Subtracting 2 from 1,3 from 2 and 1 from 3 a-b=(p-q).d..........4 b-c=(q-r).d............5 c-a=(r-p).d............6 Multiplying 4,5,6 by c,a,b c.(a-b)=c.(p-q).d...........4 a.(b-c)=a.(q-r).d...........5 b.(c-a)=b.(r-p).d.............6 a(q-r)d+b(r-p)d+c(p-q)d=0[(a(q-r)+b(r-q)+c(p-q)d=0 Now, since d is common difference it should be non zero Hence a(q-r)+b(r-q)+c(p-q)=0.

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Namrata Nath 7 years, 9 months ago

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Namrata Nath 7 years, 9 months ago

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