Problem #$7$: Suppose that a sequence $is$ defined $by$

$a_1=2,a_{n+1}=\frac{1}{6-a_n}$

$To$ show that $a_{n}is$ monotonic using mathematical induction, which $of$ the following would $be$ the second step?

$(A)$ Assume $a_{k+1}{a}_k$ and show that $\frac{1}{6-a_{k+1}}\frac{1}{6-a_k}$

$(B)$ Assume $\frac{1}{6-a_{k+1}}\frac{1}{6-a_{k+2}}$ and show that $a_k{a}_{k+1}$

$(C)$ Assume $\frac{1}{6-a_{k+1}}\frac{1}{6-a_k}$ and show that $a_{k+1}{a}_k$

$(D)$ Assume $\frac{1}{6-a_{k+2}}\frac{1}{6-a_{k+1}}$ and show that $a_{k+1}{a}_k$

$(E)$ Assume $a_{k+1}{a}_k$ and show that $\frac{1}{6-a_{k+2}}\frac{1}{6-a_{k+1}}$

$(F)$ Assume $a_k{a}_{k+1}$ and show that $\frac{1}{6-a_{k+1}}\frac{1}{6-a_{k+2}}$

$(G)$ Assume $\frac{1}{6-a_k}\frac{1}{6-a_{k+1}}$ and show that $a_k{a}_{k+1}$

$(H)$ Assume $a_k{a}_{k+1}$ and show that $\frac{1}{6-a_k}\frac{1}{6-a_{k+1}}$