Question

The number of terms between $105$ and $1000$ which are divisible by $7$ is

• A. $142$
• B. $128$
• C. $127$
• D. None of these

Answer 1

The correct option is C $127$

Clearly, the numbers between $105$ and $1000$ which are divisible by $7$ are $112,119,126,...,994$. This is an AP with first term $a=112$, common difference $d=7$ and last term $l=994$.
Let there be $n$ terms in this AP. Then,
$a_n=994\Rightarrow a+(n-1)d$

$994=112+(n-1)\times 7$

$994=105+7n$

$\therefore 7n=889$

$\therefore n=127$
Hence, Option C is correct.