Question

The number of terms between 1 to 1000 divisible by 7 are ___.

• A. 142
• B. 143
• C. 144
• D. 141

Answer 1

The correct option is A 142

The required sequence will be 7,14, 21, 28, . . . . 994.
Now, the number of terms divisible by 7 will be
994 = 7 + (n - 1)7
[$\because a_n$ = a + (n - 1) d]

Where,
a = 7,
d = 14 -7 = 7 and
n = Number of terms.

$\Rightarrow 994=7+7n-7$
$\Rightarrow 994=7n$
$\Rightarrow n=\frac{994}{7}$
$\Rightarrow n=142$

Hence, the number of terms between 1 to 1000 that are divisible by 7 are 142.