Q. 12

# In an AP, the p^{th} term is q and (p + q)^{th} term is 0. Show that its q^{th} 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.

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RD Sharma - Mathematics