Given a range [$a$,$b$], how can I find the $x$ middle numbers?
For example:
[$1$,$10$]
Now I know that the middle $2$ numbers start with "$5$", but is there any way I can find the starting number, which in this case is "$5$", given a range doing some basic calculation$?$
On
If $a$ and $b$ are integers, and you want the $x$ integers closest to the centre of $[a,b]$, then these are $$\frac{a+b-x+1}{2},\frac{a+b-x}{2}+1,\ldots,\frac{a+b+x-1}{2}$$
assuming $a+b-x+1$ is even.
If $a+b-x+1$ is odd, then there is no unique solution. What are the two middle numbers in the range $[1,9]$, for instance?
On
Simply we can use this formula like when we know the range $$\frac{(a+ b)}{2}$$
simplicity is the best policy
It is a range so in this case you can use $$\frac{(b)}{2}$$
if range is an even number
Use $$\frac{(b+1)}{2}$$
if range is an odd number
Above will give you the nth term which is your middle value of range(a, b)
If you meant the middle point of the interval then it is $\;M:=\cfrac{a+b}2\;$ . Why? Because (check this)
$$(1)\;\;a\le M\le B\;\;,\;\;\;(2)\;\;M-a=b-M$$
In fact, (2) above is the explanation for the formula for $\;M\;$ in the first line.