Find the missing number in the series4, 18, ?, 100, 180, 294, 448

The series appears to be increasing in a pattern. To find the pattern, let's look at the differences between the numbers:

18 - 4 = 14 100 - 18 = 82 180 - 100 = 80 294 - 180 = 114 448 - 294 = 154

The differences don't seem to follow a simple pattern, so let's look at the differences between the differences:

82 - 14 = 68 80 - 82 = -2 114 - 80 = 34 154 - 114 = 40

Again, no simple pattern emerges. However, if we look at the original series, we can see that each number is a multiple of 2 more than a perfect square:

4 = 2 * (1^2 + 1) 18 = 2 * (3^2 + 1) 100 = 2 * (7^2 + 1) 180 = 2 * (9^2 + 1) 294 = 2 * (11^2 + 1) 448 = 2 * (13^2 + 1)

The missing number should be 2 * (5^2 + 1), which is 52.