Sequences: A sequence is of the form $$a_1, a_2, a_3, a_4, \ldots$$ where the $a_n$ are real numbers. Technically, a sequence is a function whose domain is the set of natural numbers, and whose range is a subset of the real numbers. Sequences may be defined in various ways:

By listing, and appealing (via the three dots) to your intuition. Suppose the sequence is $$\frac{1}{2}, \frac{2}{5}, \frac{3}{10}, \frac{4}{17}, \frac{5}{26}, \frac{6}{37}, \ldots$$ Then the $n$-th term is
$a_n=$ .

Explicitly. For example, suppose $a_n=n^n$. Then $a_1=$ , $a_2=$ , and $a_3=$ .

Recursively. For example, the Fibonacci Sequence is defined by $$a_1 = a_2 = 1,\qquad a_{n+1} = a_n+a_{n-1},\qquad n = 2,3,4,\ldots .$$ Thus $a_3=$ , $a_4=$ , and $a_5=$ .

Also a sequence may or may not have a limit. For the following sequences, enter the limit, or enter the letter "D" if the sequence diverges.
$a_n = n\qquad$ .
$a_n = \frac{1}{n}\qquad$ .
$a_n = \frac{n^2+4n-5}{(2n-1)(3n-1)}$ .