In this array of five values, the relationship between each value is doubled:
[1, 2, 4, 8, 16]
Now let's say I only have the outer bounds of an array of the same size (the size here will always be five). Note that the outer values can both change in my scenario:
[1.4, x, y, z, 11]
How would I solve for x,y,z in such a way that the difference between each value in the array increases in an "accelerating" fashion? By "accelerating," I mean the values are not equidistant from each other, but the values increase in by a consistently calculated amount each time.
I believe this could technically be considered "exponential" growth, but the exponent is not a whole number, as it is in the first array example.
Since I don't even know what this is called, my tags may be totally wrong.
If the first term is $a_0$, your array is $[a_0,a_0\delta,a_0\delta^2,a_0\delta^3,a_0\delta^4]$. You know the first and last terms, so $a_0=1.4$ and $a_0\delta^4=11$. You therefore have $\delta=\sqrt[4]{11/1.4}$