if pth ,qth and rth terms of an ap are x,y and z respectively show that x(q-r)+y(r-p)+z(p-q)=0

Asked by surain bhandari | 12th Aug, 2010, 07:41: PM

Expert Answer:

ap = a + (p -1)d = x     ... (1)
aq = a + (q -1)d = y     ...(2)
ar = a + (r -1)d = z      ... (3)
(1) - (2) gives,
(p - q)d = x - y
z(p - q) = (x - y)z/d    ... (4)
Similarly,
x(q - r) = (y - z)x/d and y(r - p) = (z - x)y/d               ... (5) and (6)
Add together (4), (5) and (6),
x(q - r) + y(r - p) + z(p - q) = (y - z)x/d + (z - x)y/d + (x - y)z/d = 0
Regards,
Team,
TopperLearning.

Answered by  | 12th Aug, 2010, 10:44: PM

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