Question
Tue May 01, 2012 By: Ravi Consul
 

Q1.If the pth term of an AP is equal to q and qth term is equal to p.Then prove that the nth term is p+q-1.

Expert Reply
Wed May 02, 2012

Let the first term and common difference of the given A.P. be a and d respectively.

Given : p th term = q

? a + (p – 1) d = q ..... (1)

and g th term = p

? a + (q – 1) d = p ...... (2)

Subtracting (2) term (1), we get

(p – q)d = (q – p)

d = 1

Putting d = – 1 in equation (1), we get

a + (p – 1) (– 1) = q

? a = p + q – 1

 ? n th term = a + (n – 1) d = (p + q – 1) + (n – 1) (– 1)

= p + q – 1 – n + 1 = p + q – n

 ? n th term of the given A. P. is (p + q – n)

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