Chapter 11 - Sequences; Induction; the Binomial Theorem - Section 11.2 Arithmetic Sequences - 11.2 Assess Your Understanding - Page 834: 9

Common difference of $-2$ . The first four terms are: $4, 2,0,-2$

We need to substitute $1, 2, 3,$ and $4$ for $n$ into the given equation to find the first four terms. $c_1=6-(2)(1)=6-2=4 $ $c_2=6-(2)(2)=6-4=2 $ $c_3=6-(2)(3)=6-6= 0 $ $c_4=6-(2)(4)=6-8=-2 $ We can see that the common difference is $-2$ (decreases by 2 each time). Thus, the sequence is arithmetic with a common difference of $-2$ .