Question
How many multiples of $4$ lie between $10$ and $205$ ?
✓
Answer
Let the number of multiples of $4$ lie between $10$ and $205$ be $n$.
$\therefore$ first multiples $(a) =12$
last multiples $( l )=204$
Common difference $( d )=4$
$\because l=a+(n-1) d$
$204=12+(n-1) 4$
$\Rightarrow 4(n-1)=204-12$
$\Rightarrow 4(n-1)=192 $
$\Rightarrow(n-1)=\frac{192}{4}=48$
$\Rightarrow n=48+1=49$
Hence, required number of multiples $=49$.
$\therefore$ first multiples $(a) =12$
last multiples $( l )=204$
Common difference $( d )=4$
$\because l=a+(n-1) d$
$204=12+(n-1) 4$
$\Rightarrow 4(n-1)=204-12$
$\Rightarrow 4(n-1)=192 $
$\Rightarrow(n-1)=\frac{192}{4}=48$
$\Rightarrow n=48+1=49$
Hence, required number of multiples $=49$.
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