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Q.

Let an be the nth  term of an A.P if ∑r=1100 a2r=α and ∑r=1100 a2r−1=β then the common  difference of the A.P is:

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a

α−β200

b

α−β

c

α−β100

d

β-α

answer is C.

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Detailed Solution

α=a2+a4+a6+……………+a200β=a1+a3+a5+………..+a199α−β=a2−a1+a4−a3+a6−a5+……..+a200−a199α−β=d+d+d+………….+d=100dd=(α−β)100
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Let an be the nth  term of an A.P if ∑r=1100 a2r=α and ∑r=1100 a2r−1=β then the common  difference of the A.P is: