Let $$a_n=\frac{1}{5 n^2 - 610 n + 18610}.$$ The infinite sequence $\big( a_n\big)_{n=1}^{\infty}=\big(a_1,a_2,a_3,\ldots\big)$ is not monotone.

Is there a positive integer $N$ so that, when one drops the first $N-1$ terms from the original sequence, the result $$\big( a_n\big)_{n=N}^{\infty}=\big(a_N,a_{N+1},a_{N+2},\ldots\big),$$ IS a monotone sequence?

If such an $N$ exists give the least value of $N$. If it does not exist then enter NA.

Describe the infinite sequence $\big(a_N,a_{N+1},a_{N+2},\ldots\big)$. (Use the $N$ from the previous question, if it exists.)

$\big(a_N,a_{N+1},a_{N+2},\ldots\big)$ is Select monotone increasing. monotone decreasing. cannot be monotone.