Let a1,a2,a3,…………….a49be in A.P. such that∑k=012 a4k+1=416 and a9+a43′=66 ,a12+a22+…………+a172=140m then  m is equal to 

Let a1,a2,a3,.a49be in A.P. such thatk=012a4k+1=416 and a9+a43=66 ,a12+a22+...+a172=140m then  m is equal to 

  1. A

    33

  2. B

    66

  3. C

    68

  4. D

    34

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    Solution:

    k=012a4k+1=416

    a1+a5++a49=416 132a1+a49=416

    As a49=a1+48d so we have

    1322a1+48d=416a1+24d=32     …………………... (i) 

    Given, a9+a43=66a1+8d+a1+42d=66

    a1+25d=33         …………………………….…(ii)

    The equation (i) and (ii) gives a1=8,d=1

    Now, a12+a22+..+a172=82+92+.+242=12+22+..+24212+22+.+72=242549678156=4760=34(140)

     m=34

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