In an AP, the pth term is q and (p + q)th term is 0. Show that its qth

1.	In an AP, the pth term is q and (p + q)th term is 0. Show that its qth term is p.
Answer» Given: p^th term is q and (p + q)^th term is 0. To prove: q^th term is p. p^th term is given by q = a + (p - 1) × d……equation1 (p + q)^th term is given by 0 = a + (p + q - 1) × d 0 = a + (p - 1) × d + q × d Using equation1 0 = q + q × d d = - 1 Put in equation1 we get a = q + p - 1 q^th term is ⟹ q + p - 1 + (q - 1) × ( - 1) ⟹ p Hence proved.

In an AP, the pth term is q and (p + q)th term is 0. Show that its qth term is p.

Answer»

Given: p^th term is q and (p + q)^th term is 0.

To prove: q^th term is p.

p^th term is given by

q = a + (p - 1) × d……equation1

(p + q)^th term is given by

0 = a + (p + q - 1) × d

0 = a + (p - 1) × d + q × d

Using equation1

0 = q + q × d

d = - 1

Put in equation1 we get

a = q + p - 1

q^th term is

⟹ q + p - 1 + (q - 1) × ( - 1)

⟹ p

Hence proved.