The sum of first n terms of an AP is m and the sum of first m terms is n The sum of first m n t...........

Mathematics (NDA) Arithmetic progression

The sum of first n terms of an AP is m and the sum of first m terms is n .The sum of first (m +n) terms is ?

(n +m)

-(n+ m)

(n -m)

(m -n)

Given , m = n/2 [ 2a +(n-1)d ]

n = m/2 [ 2a + (m-1)d ]

On subtracting , we get ,

2(m- n ) = 2an +n(n-1)d -2am -m(m-1)d

Or 2(m-n) = (n- m)(n +m -1)d + 2a(n -m)

Or -2 = (n +m -1)d +2a ……(1)

Now , sum of first (n +m) terms is

= (n +m)/2 [ 2a +(n+ m -1)d ]

= ( n +m)/2 × (-2) ( from (1) )

= - ( n +m )

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