I'm not a mathematician, so I don't know the terminology.
I'm working in excel and I need to create a formula to fill in a sequence of numbers, where I know the beginning and end of the sequence, and the numbers in between are evenly spaced.
Basically this means that the first number (always lowest) is 0% and the highest number (always highest) is 100%, and I need to get the numbers in between.
For example with 3 .. .. .. 7, that would be 3 4 5 6 7.
Another example: 5 .. .. .. 15, that would be 5 7.5 10 12.5 15.
Each of the .. will have the same formula where I know on beforehand how much of the percentage it is, for example: 0% 25% 50% 75% 100%
What formula do I need to create this sequence?
If it helps, either reference to l,h for lowest and highest in your formula, or A1 and A5 if you prefer an excel style formula.
Best Answer
If the sequence is $l, a_1, a_2, \dots, a_n, h$ and the $a_k$ are the numbers to be determined, then there are $n+1$ gaps of equal length:
$$g : =a_1 - l = a_2 - a_1 = \dots = a_n - a_{n-1} = h - a_n.$$
It follows that $a_k = l + k\cdot g$ and
$$(n+1)\cdot g = h - l \implies g = \frac{h-l}{n+1}.$$
So the $k$-th missing number is
$$a_k = l+\frac{k(h-l)}{n+1}.$$