Considering 2K = 1440p, has twice the pixels compared to 1080p, 4k has four times as many, why does 8k not follow this trend?
First off, 2K is not 1440p, it is 2048 x 1080p. 4K is 4096 x 2160p. (Note that UHD = 3840 x 2160p...4K and UHD are like US and Canadian dollars--they are both dollars, but they have different values.)
It's simple math: when you have a straight line and you make it twice as long, the new length is 2x the original length. When you have a rectangular area and you double both the length and the width in order to keep the same aspect ratio, the new area = (2L) * (2W) = 4 * (L*W)
When you double something twice, you do it again:
2*(2L) * 2*(2W) = 4 * 4 * (L*W) = 16 * (L * W)