If the sum of the first `100` terms of an `AP` is `-1` and the sum of even terms lying in first `100` terms is `1`, then which of the following is not

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If the sum of the first `100` terms of an `AP` is `-1` and the sum of even terms lying in first `100` terms is `1`, then which of the following is not true ?
A. Common difference of the sequence is `(3)/(50)`
B. First term of the sequence is `(-149)/(50)`
C. `100^(th)` term `=(74)/(25)`
D. None of these


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Salim Ahmed Kawsar

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Correct Answer - D
`(d)` `x_(1)+x_(2)+x_(3)+……+x_(100)=(100)/(2)(x_(1)+x_(100))=-1`
`impliesx_(1)+x_(100)=-(1)/(50)`
`x_(2)+x_(4)+…+x_(100)=(50)/(2)(x_(1)+d+x_(100))=1`
`impliesx_(1)+x_(100)+d=(1)/(25)`
`impliesd=(3)/(50)` ltbr `x_(1)+x_(1)+99d=(-1)/(50)`
`impliesx_(1)=(-149)/(50)`
`x_(100)=x_(1)+99d`
`=(-149)/(50)+99xx(3)/(50)`
`=(74)/(25)`

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