Consider the following statements  I. If an denotes  the  nth  term  of an AP, then  an=an+k+an−k2   II. In an  AP, if the Sum  of m  terms  is equal to the sum of n terms, then the sum of(m  + n)  terms is always  zero. Which of the  statement is given  above is/are correct?

Consider the following statements  I. If an denotes  the  nth  term  of an AP, then  an=an+k+ank2   II. In an  AP, if the Sum  of m  terms  is equal to the sum of n terms, then the sum of(m  + n)  terms is always  zero. Which of the  statement is given  above is/are correct?

  1. A

    Only I

  2. B

    only II

  3. C

    Both I  and II

  4. D

    None of these

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    Solution:

    Statement I Since, nth term of an AP is αn an=an+k+ank2 AM=a+b2  Statement II Let a be the first term and d be the common difference of an AP.

     According to the given condition, 

    Sm=Sn         m2[2a+(m1)d]=n2[2a+(n1)d]     (mn)2a+m2n2m+nd=0     (mn)[2a+(m+n1)d]=0    ...(i)     S(m+n)=m+n2[2a+(m+n1)d]=0=    m+n2(0)     [from eq.(i)]=0

     

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