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