Question

If $a,b,c$ be the $p^{th},q^{th}$ and $r^{th}$ terms respectively of an A.P, then $a(q-r)+b(r-p)+c(p-q)=$

• A. 1
• B. -2
• C. 0
• D. 2

Answer 1

The correct option is C 0

From given, we have,

$a=A+(p-1)D$

$b=A+(q-1)D$

$c=A+(r-1)D$

Given,

$a[q-r]+b[r-p]+c[p-q]$

$=[A+(p-1\left)D\right][q-r]+[A+(q-1\left)D\right][r-p]+[A+(r-1\left)D\right][p-q]$

$=A[q-r+r-p+p-q]+D\left[\right(p-1\left)\right(q-r)+(q-1\left)\right(r-p)+(r-1\left)\right(p-q\left)\right]$

$=A\times 0+D\times 0$

$=0$