This topic here:

in-the-sequence-x0-x1-x2-xn-each-term-from-x1-to-xk-126564.htmlgot me thinking about what does "n" actually mean? Before I was 100% sure that "n" denotes the rank that the element holds in a set. But in the above example the 11th element had an "n" of 10. Not 11, but 10. So no, "n" does not denote the rank that the element holds in a set.

So what does "n" denote then?So I decided to play around with numbers.

Example: imagine an AP with difference (d)=3 and the first term being 2

If the sequence begins with "n"=0

Rank order: first-second-third

"n": 0-1-2

Actual numbers: 2-5-8

If the sequence begins with n=1

Rank order: first-second-third

"n": 1-2-3

Actual numbers: 5-8-11

If the sequence begins with n=4

Rank order: first-second-third

"n": 4-5-6

Actual numbers: 14-17-20

So what I take away from this is:

The formula

Last term - first term = (n-1) times difference is not correct. Proof:

Let's try it for the first sequence:

For third term: 8-2 = (2-1)*3 = doesn't work

Let's try it for the second sequence:

For third term: 11-5 = (3-1)*3 = WORKS

Let's try it for the third sequence:

For third term: 20-14 = (6-1)*3 = doesn't work

Ok so now let's change the formula to

Last term - first term = (RANK-1) times differenceThen it works for all three, because in all three cases rank is the same = 3.

So to summarise my questions:

1. In a set, what exactly does "n" stand for?2. Why do we need it in a set when we could have just used RANKS instead?3. When a sequence exercise tells us n>1 or n>9 or n>0, why do they do it? What are we supposed to take away from this?Hope this makes sense!