What number is needed to complete this pattern 107 98 90 83 77 68 65?

Answer 1

The original set would be 107, 98, 90, 83, 77, x, 68, and 65. The pattern of this set of numbers is that the first term is subtracted by 9, the next by 8, the next by 7, and so on. Therefore, the term x would be 72, which is 5 less than 77 and 4 more than 68.

Answer 2

Not sure about completing the pattern since there is no reason for it to stop after the next number.

There is no polynomial solution for polynomials of order 5 of lower. The simplest answer is obtained by fitting the following polynomial of order 6:

U(n) = (4*n^6 - 155*n^5 + 1345*n^4 - 5825*n^3 + 13288*n^2 - 17060*n + 34080)/240 for n = 1, 2, 3, ...