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

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

$$a_2=a_1+2+1=2+3=5$$

$$a_3=a_2+3+1=5+4=9$$

$$a_4=a_3+4+1=9+5=14$$

$$a_5=a_4+5+1=14+6=20$$

$$a_6=a_5+6+1=20+7=27$$

$$a_7=a_6+7+1=5+4=27+8=35$$

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

$$b_2=b_1(2+1)=3$$

$$b_3=b_2(3+1)=12$$

$$b_4=b_3(4+1)=60$$

$$b_5=b_4(5+1)=360$$

$$b_6=b_5(6+1)=2520$$

$$b_7=b_6(7+1)=20160$$