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The concept of "n" within a SEQUENCE - don't get it?

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The concept of "n" within a SEQUENCE - don't get it? [#permalink] New post 26 Jul 2014, 07:27
This topic here: in-the-sequence-x0-x1-x2-xn-each-term-from-x1-to-xk-126564.html
got 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 difference
Then 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!
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The concept of "n" within a SEQUENCE - don't get it? [#permalink] New post 26 Jul 2014, 07:47
Hello imoi,

The value of n is just a place holder for a number of the sequence. In the example your provided via your link, since the start of the sequence started when n=0, then the n=10 is the 11th term. From a sequence, it is important to know where it started or stopped to determine the value of n, i.e. if the first term was n=1, then the final answer would have been n=11.

I am not sure what you are trying to prove for with your example. In terms of \frac{(last term - first term)}{difference} = number of steps between the two values.
Example 1: \frac{(8-2)}{3}= 2 -> two steps between the two values, if you knew that the first term is n=0, then the 3rd term is n=2. This would apply for all your examples.

Hope this helps. If not, can you please reword your statement so its a bit clearer?

Last edited by wunsun on 26 Jul 2014, 08:09, edited 1 time in total.
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Re: The concept of "n" within a SEQUENCE - don't get it? [#permalink] New post 26 Jul 2014, 08:03
wunsun wrote:
Hello imoi,

The value of n is just a place holder for a number of the sequence. In the example your provided via your link, since the start of the sequence started when n=0, then the n=10 is the 11th term. From a sequence, it is important to know where it started or stopped to determine the value of n, i.e. if the first term was n=1, then the final answer would have been n=11.

I am not sure what you are trying to prove for with your example. In terms of (last term - first term)/difference = number of steps between the two.
Example 1 = (8-2)/3 = 2 -> two steps between the two values, if you knew that the first term is n=0, then the 3rd term is n=2. This would apply for all your examples.

Hope this helps. If not, can you please reword your statement so its a bit clearer?


Thanks a million for your reply. I was worried that I didn't communicate my issue too effectively.

I definitely understand what you are saying about knowing where the sequence starts. I just don't get the idea of the "zeroth" term - why does it even exist?

Also for some problems, such as this one:
the-sequence-a1-a2-a3-a4-a5-is-such-that-an-a-n-1-5-for-166830.html
we are given more severe constrains (above or equal to 2 and below or equal to 5). How does that impact my solution to this problem? It doesn't really, does it? So what's the point of writing that?

Sorry if I am retarded haha
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Re: The concept of "n" within a SEQUENCE - don't get it? [#permalink] New post 26 Jul 2014, 08:16
No problem. We each have our own weaknesses and as long as we own up to them, we get better and improve.

In terms of the example your provided in the last post, no, the 2\leq{n}\leq{5} does not restrict the question beyond what you would normally do. I am not sure why it was placed for this question, but sometimes GMAT puts in mathematical restrictions to ensure that problem is functional, i.e. x\neq{2} for equation \frac{(x+3)}{(x-2)}. This ensure that the value of the denominator cannot ever be zero and makes the question functional for a lack of a better word.
Re: The concept of "n" within a SEQUENCE - don't get it?   [#permalink] 26 Jul 2014, 08:16
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