2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 4 16 36 64 100 144 196 256 324 400 484 576 676 784 900 1024 220 1540 4960 5980 sum of even integers 2 to 30 = 4960 sum of even integers 2 to 32 = 5980 This question assumes a false conclusion.
Any number can be the next number. It is easy to find a rule based on a polynomial of order 2 such that the first two numbers are 1 and 247, and followed by the chosen next number. There are also non-polynomial solutions. Short of reading the mind of the person who posed the question, there is no way of determining which of the infinitely many solutions is the "correct" one.So, if you want the next number to be 1, use the rule t(n) = -246n^2 + 984n - 737You want 9, use the rule t(n) = -242n^2 + 972n - 729You want 99, use the rule t(n) = -197n^2 + 837n - 639You want 765, use the rule t(n) = 136n^2 - 162n + 27and so on.