Question
How many three digit numbers are divisible by 7?
✓
Answer
The first three digit number which is divisible by $7$ is $105$ and the last digit which is divisible by $7$ is $994 .$
This is an A.P. in which $a=105, d=7$ and $t_n=994$.
We know that $n^{\text {th }}$ term of A.P is given by
$t_n = a + (n - 1)d.$
$\Rightarrow 994 = 105 + (n - 1)7$
$\Rightarrow 889 = 7n - 7$
$\Rightarrow 896 = 7n$
$\Rightarrow n = 128$
$\therefore$ There are $128$ three digit numbers which are divisible by $7 .$
This is an A.P. in which $a=105, d=7$ and $t_n=994$.
We know that $n^{\text {th }}$ term of A.P is given by
$t_n = a + (n - 1)d.$
$\Rightarrow 994 = 105 + (n - 1)7$
$\Rightarrow 889 = 7n - 7$
$\Rightarrow 896 = 7n$
$\Rightarrow n = 128$
$\therefore$ There are $128$ three digit numbers which are divisible by $7 .$
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