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If pth term of an A.P.is q and the qth term is p prove that its nth term is (p+q-n)

Posted by Hema Pandey 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

Let a be the first term and d be the common difference of the given A.P. Then,
p^th term = q {tex}\Rightarrow{/tex}a + (p-1) d = q ...(i)
q^th term = p {tex}\Rightarrow{/tex}a + (q-1) d = p ...(ii)
Subtracting equation (ii) from equation (i), we get
(p - q) d = (q - p) {tex}\Rightarrow{/tex} d = -1
Putting d = - 1 in equation (i), we get
a + ( p-1) × (-1) = q
⇒ a = (p + q - 1)
nth term = a + (n -1 )d
= (p + q - 1)+ (n -1) × (-1)
= p + q - 1 -n + 1
= (p + q - n)

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