How many $3$ digit numbers are there in between $100$ to $550$?

Given: $3$ digit numbers between $100$ to $550$.

To do: To find the number of $3$ digit numbers between $100$ to $550$.

Solution:

$3$ digit numbers between $1004 to $550$ are: $101\ 102,\ 103,\ .......\ 549$.

It is an A.P., here first term $a=101$, last term $l=549$, common difference $d=1$

As known $l=a+( n-1)d$, here $n$ is the number of terms.

$\Rightarrow 549=101+( n-1)1$

$\Rightarrow n-1=549-101$

$\Rightarrow n-1=448$

$\Rightarrow n=448+1$

$\Rightarrow n=449$

Thus, there are $449$ numbers between $100$ to $550$.  

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Updated on: 10-Oct-2022

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