consider the arithmetic sequence: 6, 2, -2, -6, ... if n is an integer, which of these functions generate…

Explanation:

Step1: Recall the formula for an arithmetic - sequence

The general formula for an arithmetic sequence is $a(n)=a(1)+(n - 1)d$, where $a(1)$ is the first - term and $d$ is the common difference. For the sequence $6,2, - 2, - 6,\cdots$, $a(1)=6$ and $d=2 - 6=-4$.

Step2: Test option A

When $n = 0$, $a(0)=10-4\times0 = 10\neq6$. So option A is incorrect.

Step3: Test option B

When $n = 1$, $b(1)=10-4\times1=6$. When $n = 2$, $b(2)=10-4\times2 = 10 - 8 = 2$. When $n = 3$, $b(3)=10-4\times3=10 - 12=-2$. When $n = 4$, $b(4)=10-4\times4=10 - 16=-6$. So option B is correct.

Step4: Test option C

When $n = 2$, $c(2)=18-4\times2=18 - 8 = 10\neq2$. So option C is incorrect.

Step5: Test option D

When $n = 3$, $d(3)=14-4\times3=14 - 12 = 2\neq - 2$. So option D is incorrect.

Answer:

B. $b(n)=10 - 4n$ for $n\geq1$