The sum of `25` terms of an `A.P.`, whose all the terms are natural numbers, lies between `1900` and `2000` and its `9^(th)` term is `55`. Then the fi

Monjur Alahi

The sum of `25` terms of an `A.P.`, whose all the terms are natural numbers, lies between `1900` and `2000` and its `9^(th)` term is `55`. Then the first term of the `A.P.` is
A. `5`
B. `6`
C. `7`
D. `8`


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Salim Ahmed Kawsar

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Correct Answer - C
`(c )` Let the first term be `a` and the common difference `d`.
Then it is given that `a+8d=55` and ……..`(i)`
`1900 lt (25)/(2)(2a+24d) lt 2000`
`:.1900 lt 25(a+12d) lt 2000`
`implies1900 lt 25(a+8d)+25xx4d lt 2000`
`implies1900 lt 25xx55+100d lt 2000`
`implies(525)/(100) lt d lt (625)/(100)`
`impliesd=6` as `d` is an integar
`:. a=55-8xx6=7`

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