Chapter 1.2, Problem 26ES

The nth-term formula

$a_n=\frac{n\left(n-1\right)\left(n-2\right)\left(n-3\right)\left(n-4\right)}{4\cdot 3\cdot 2\cdot 1}+2n$ generates 2, 4, 6, 8, 15 for $n=\text{ 1},\text{ 2},\text{ 3},\text{ 4},\text{ 5}$. Make minor changes m to above formula to produce an nth-term formula (with $n=\text{ l},\text{ 2},\text{ 3},\text{ 4},\text{ and 5}$

) that will generate the following finite sequences.

a. 2, 4, 6, 8, 20

b. 2, 4, 6, 8, 30