Question

Hii Friends ..
please answer..

if p th term of A.P is q , and q rh term of A.P is p . Then prove that it's nth term is ( p + q - n ) ..​

Answer 1

pth term = a+(p-1)d = q

qth term = a+(q-1)d = p

nth term = a+(n-1)d

p-q = a+(p-1)d-a-(q-1)d

= a+dp-d-a-dq+d

= dq-dp

p-q = d(q-p)

d = -1

a-p+1= q (From pth term)

a = p+q-1

nth term = p+q-1-n+1

= p+q-n

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