Question

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​

Answer 1

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)]

Answer 2

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