How many multiples of 4 lie between 10 and 250? - Vidyadip

Question

How many multiples of $4$ lie between $10$ and $250?$

✓

Answer

Let,
Multiple of $4$ lie between $10$ and $250$
$12, 16, 20, ..... 248$
we know $a_n= a+ (n - 1)d$
Here,
First term $a= 12$
Difference $d = 16 - 12 = 4$
$ \text { and Last } \mathrm{n}^{\text {th }} \text { term } \mathrm{a}_{\mathrm{n}}=248 $
$ \text { Then, } \mathrm{a}_{\mathrm{n}}=\mathrm{a}+(\mathrm{n}-1) \mathrm{d} $
$ \Rightarrow 248=12+(\mathrm{n}-1) 4 $
$ \Rightarrow 248=12+4 \mathrm{n}-4 $
$ \Rightarrow 4 \mathrm{n}=248-12+4 $
$ \Rightarrow 4 \mathrm{n}=240 $
$ \Rightarrow \mathrm{n}=60$
Hence, multiple of $4$ lies between $10$ and $250$ is $60.$

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