Question

if p th,qth and r th terms of an ap are a, b and c respectively then show that (a-b)r+(b-c)p+(c-a) q=0​

Answer 1

Answer:

Step-by-step explanation:

First term = m

p th term = m + (p-1)d = a

q th term = m + (q-1)d = b

r th term = m + (r-1)d = c

(a-b)r+(b-c)p+(c-a) q

=(m + (p-1)d -m - (q-1)d )r +(m + (q-1)d-m -(r-1)d)p+(m + (r-1)d-m - (p-1)d)q

=(p-q)dr+(q-r)dp+(r-p)dq

= (pr-qr+qp-rp+rq-pq)d = 0×d = 0

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