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`
Text Solution
Verified by Experts
The correct Answer is:
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`
