Question
How many three digit natural numbers are divisible by $7 ?$
✓
Answer
Following are the three digit natural numbers divisible by $7 :$
$105,112,119,126.$ The given series is $A.P.$
First term $(a)=105$
Common diff $(d)=7$
$n^{\text {th }} \text { term }\left(a_n\right)=994$
It is known that the term of an $A.P.$ is given by,
$a_n=a+(n-1) d$
Substituting $a=105, d=7$ and $a_n=994$
$994=105+(n-1) 7$
$\Rightarrow 994=105+7 n-7$
$\Rightarrow 994=98+7 n$
$\Rightarrow 7 n=994-98$
$\Rightarrow 7 n=896$
$\Rightarrow n=128$
Thus $128$ three digit natural numbers are divisible by $7 .$
$105,112,119,126.$ The given series is $A.P.$
First term $(a)=105$
Common diff $(d)=7$
$n^{\text {th }} \text { term }\left(a_n\right)=994$
It is known that the term of an $A.P.$ is given by,
$a_n=a+(n-1) d$
Substituting $a=105, d=7$ and $a_n=994$
$994=105+(n-1) 7$
$\Rightarrow 994=105+7 n-7$
$\Rightarrow 994=98+7 n$
$\Rightarrow 7 n=994-98$
$\Rightarrow 7 n=896$
$\Rightarrow n=128$
Thus $128$ three digit natural numbers are divisible by $7 .$
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