Multiple Choice Questions on If the sum of n terms of an AP is the same as the sum of its m terms then the sum of its n m te........... for NDA Exam Preparation

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Multiple Choice Questions

If the sum of n terms of an AP is the same as the sum of its m terms then the sum of its n m te...........

Mathematics (NDA) Arithmetic progression
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    If the sum of n terms of an AP is the same as the sum of its m terms, then the sum of its (n+m) terms is?

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    Explanation:

    Given ,    Sn = Sm 

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

     Or  (1-n -m)d = 2a 

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

    = (n +m)/2[2a – (1- n- m )d] 

    = (n +m)/2 [2a -2a] 

    = 0 

    By: bhavesh kumar singh
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