prove that:
Asked by vaishnavi
| 29th Aug, 2012,
04:23: PM
Expert Answer:
Let A and D be the first term and common difference of A.P.
From the given information, we have:
A + (p 1) D = a
(1)
A + (q 1) D = b
(2)
A + (r 1) D = c
(3)
a (q r) + b (r p) + c (p q)
= [A + (p 1) D] (q r) + [A + (q 1) D] (r p) + [A + (r 1) D] (p q)]
= A (q r) + (p 1) (q r)D + A (r p) + (q 1) (r p) D + A (p q) + (r 1) (p q) D
= A (q r + r p + p q) + D (pq pr q + r + qr pq r + p + pr rq p + q)
= A (0) + D (0)
= 0
Let A and D be the first term and common difference of A.P.
From the given information, we have:
A + (p 1) D = a
(1)
A + (q 1) D = b
(2)
A + (r 1) D = c
(3)
a (q r) + b (r p) + c (p q)
= [A + (p 1) D] (q r) + [A + (q 1) D] (r p) + [A + (r 1) D] (p q)]
= A (q r) + (p 1) (q r)D + A (r p) + (q 1) (r p) D + A (p q) + (r 1) (p q) D
= A (q r + r p + p q) + D (pq pr q + r + qr pq r + p + pr rq p + q)
= A (0) + D (0)
= 0
Answered by
| 29th Aug, 2012,
05:06: PM
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