Question

if pth term is q and q th term is p of arithmetic progression, than prove that ( p+ q) th term is 0​

Answer 1

Answer:

In an AP,

pth term = q, qth term = p

To prove,

nth term = (p+q-n)

= q

⇒ a+(p−1)d = q ...(1)

= p

⇒ a+(q−1)d = p ...(2)

Solving these equations, we get,

pd - qd = q - p

(p-q)d = -(p-q)

⇒ d=−1

From equation (1),

a = (p+q−1)

Thus,

= a + (n - 1)d

= (p + q - 1) + (n - 1) (-1)

= P + q - 1 + 1 - n

∵ nth term or = (p+q−n)