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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+q1.
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)