Question

Continue the two sequences of numbers below and find an equation to each of the sequences: n 1 2 3 4 5 6 7 Equation an 2 5 9 14 20 27 bn 1 3 12 60 360 2520 

Answer 1

$$2, 5, 9, 14, 20, 27,35, 44, 54,...$$

$$a_n=a_{n-1}+(n+1), n\geq2, a_1=2$$

$$1, 3, 12, 60, 360, 2520,20160,181440,...$$

$$b_n=b_{n-1}(n+1), n\geq2, b_1=1$$

$$b_n=\dfrac{(n+1)!}{2}, n\geq1$$