Question

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

Answer 1

hope it might help you

Answer 2

Solution :

Let a be the first term and d be the

common difference of the given A.P.

Then ,

pth term = q => a + ( p-1 )d = q ---( 1 )

q th term = p => a + ( q - 1 )d = p---( 2 )

Subtracting equation ( 2 ) from

equation ( 1 ), we get

( p - q )d = ( q - p )

=> d = ( q - p )/( p - q )

=> d = [ -( p - q ) ]/( p - q )

=> d = -1

Put d = -1 in equation ( 1 ) , we get

a + ( p - 1 )( -1 ) = q

=> a = p - 1 + q

Therefore ,

n th term = a + ( n-1)d

= p - 1 + q + ( n - 1 )( -1 )

= p - 1 + q - n + 1

= ( p + q - n )

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