If pth, qth and rth term of an AP are a, b, c respectively, the show that: (a-b)r + (b-c)p + (c-a)q = 0
Answers
Answered by
9
Answer:
Step-by-step explanation:
Let A be the first term of the A.P. and D be the common difference of the A.P.
Given that,
a = pth term
Therefore,
b = qth term
Therefore,
c = rth term
Therefore,
LHS = (a-b)r +(b-c)p + (c-a)q
= ar - br + bp - cp + cq - aq
= -(aq - ar) - (br - bp) - (cp - cq)
= - [a(q - r)+ b(r - p) + c(p - q)]
shashankkamlesh:
Man what are you solving. read the question properly
Answered by
3
Step-by-step explanation:
Let A be first term and D be common diffrence
By given data
a = A+(p-1)d
b = A+(q-1)d
c = A+(r-1)d
a-b=(p-q)d×r =rpq - qrp ------------》1
b-c=(q-r)d×p = pqd - prd-----------》2
c-a=(r-p)d× q = qrd - pad----------》3
LHS=adding 1+2+3 every term get cancelled = 0
THUS PROVED
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