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How many three digit numbers are divisible by 7?
To do:
We have to find the number of three digit numbers divisible by 7.
Solution:
Let $n$ be the number of terms which are divisible by $7$.
Let $a$ be the first term and $d$ be the common difference.
Multiples of 7 are $7, 14, ....., 98, 105, ....., 994, 1001, ......$
The first three-digit number divisible by $7$ is $105$.
This implies,
$a = 105, d = 7$, last term $a_n = 994$
$a_n = a + (n – 1) d$
$994 = 105 + (n – 1) \times 7$
$994- 105 = 7n – 7$
$7n = 889 +7$
$7n = 896$
$n=\frac{896}{7}$
$n=128$
Therefore, 128 three-digit numbers are divisible by 7.
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