What is the next 5 terms after -5 -15 -45 -135?

Answer 1

There are infinitely many polynomials of order 4 that will give these as the first four numbers and any one of these could be "the" rule. 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. The simplest polynomial of order 3 isU(n) = 3/5*(-4*n^3 + 18*n^2 - 32*n + 15) for n = 1, 2, 3, ...and accordingly, the next 5 terms would be -325, -655, -1165, -1895 and -2885.
However, in this particular example, it is easy (?) to see that the pattern is -5*3^(n-1) so that the next 5 terms are -405, -1215, -3645, -10935 and -32805.