What is the next number in the series-3-14-39-84-155?

Answer 1

Given any number it is easy to find a polynomial rule of order 5 such that the first five numbers are as listed in the question and the sixth is the given number. That is, I can find a rule so that any number can be the "next" in the sequence.

The simplest solution, using a cubic equation is

Un = n3 + n2 + n for n =1, 2, 3, ...

Accordingly, the next term is 258.

Answer 2

The next number in the series is 254. The pattern in the series is adding the square of consecutive natural numbers to each term. Starting from -3, -3 + 1^2 = -3 + 1 = -2. Then, -2 + 2^2 = -2 + 4 = 2, and so on.