Question

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

• A. 5
• B. 6
• C. 7
• D. 8

Answer 1

The correct option is C 7

let first term of an AP be a common difference be $d$

we have $a+8d=55$........(1)

Also $\frac{25}{2}(a+a+24d)$=sum of $25$ terms of an AP

$1900<\frac{25}{2}(2a+24d)<2000$

$1900<25(a+12d)<2000$

$76<a+12d<80$

$76<55-8d+12d<80$

$21<4d<25\Rightarrow \frac{21}{4}<d<\frac{25}{4}$

put $d=6$ in (1) we have

$a+48=55\Rightarrow a=7$.