Question
How many three-digit numbers are divisible by $7?$
✓
Answer
All $3$-digit numbers divisible by $7$ are
$105,112,119, ...,994.$
Clearly, these numbers form an $AP$ with $a = 105, d = (112-105) = 7$ and $l = 994.$
Let it contain $n$ terms. Then,
$T_n= 994 \Rightarrow a + (n-1)d = 994$
$\Rightarrow 105 + (n -1) 7 = 994$
$\Rightarrow 98 + 7n = 994$
$\Rightarrow 7n = 896$
$ \Rightarrow n = 128.$
Hence, there are $128$ three-digit numbers divisible by $7.$
$105,112,119, ...,994.$
Clearly, these numbers form an $AP$ with $a = 105, d = (112-105) = 7$ and $l = 994.$
Let it contain $n$ terms. Then,
$T_n= 994 \Rightarrow a + (n-1)d = 994$
$\Rightarrow 105 + (n -1) 7 = 994$
$\Rightarrow 98 + 7n = 994$
$\Rightarrow 7n = 896$
$ \Rightarrow n = 128.$
Hence, there are $128$ three-digit numbers divisible by $7.$
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