following number series 5,6,15,50 what is the next number?

Question

what should come in place of the question mark?in the following number series? 5,6,15,50 1) 207 2) 157 3) 205 4)none

Answer 1

If n is the position of the number in the series, the following recursive pattern seems to apply:

a_n+1=(n+1)a_n+2n+1, a₀=5.

Using the formula, a₁=1×5+1=6, a₂=2×6+3=15, a₃=3×15+5=50, a₄=4×50+7=207, answer (1).