Getting the 557th element of a table

Question

Make a table with elements $\sin(\sqrt{8 n}/4) + r\, $for $n$ from $1$ to $1000$, where $r$ is a random real number between $-0.1$ and $0.1$ that is different for each value of $n$. Also make a plot of all the points of this table. What is the $557^{th}$ element of this table?

Everything is working well, but I can't get the 557th element of the table. I've tried to use the Select command.

Select[TableSin[Sqrt[(a*n)/4]] + Random[Real, {-0.1, 0.1}], {n, 1, 1000}] ,557]

but it's not working. I can't figure out how to fix it.

Can anyone give me some hints?

Answer 1

Select is wrong in this case, you can't use it to get the n-th element of a list without using additional helper functions.

You'll get the most out of this exercise by looking at Part, which is a very flexible function for extracting elements out of a list based on their position, for example

x = {1,1,2,3,5,8,13,21,34,55}

(* Explicit syntax. Extracts the 3rd element out of a list
   (first element has index 1). *)
Part[x, 3]
(* ==> 2 *)

(* Syntactic sugar: using [[ ]] for Part *)
x[[3]]
(* ==> 2 *)

Part can do much more, e.g. extracting ranges, submatrices and so on. While not necessary to solve this problem, I highly recommend reading a few paragraphs in the Mathematica help - you will need it again soon. :-)

For the fun of it, here's the easiest way of doing the same task with Select instead of Part I could come up with:

x = {1, 1, 2, 3, 5, 8, 13, 21, 34, 55}
Select[
    MapIndexed[{#1, First@#2} &, x],
    Last[#] == 3 &
] // First // First
(* ==> 2 *)

(Manually index the list wasting a ton of memory, then pick the element and discard the indexing again.)