Staff Versus Members! (Current record: 200)

[anoni]

1. I GOT IT RIGHT. I highlighted it

1.
Ok lets see, first it doesn't seem to be an arithmetic sequence so let look at the gaps between each number
7 - 11 - 15 - 19
So it is arithmetic where the rate increases by 4 each step.

General arithmetic sequence formula is An = a + (n - 1)r
However for this sequence it's actually
An = 7 + 4(n - 1) + 7 + 4(n - 2) + ... + 7 - 1
Factorizing we get
An = -1 + 7(n - 1) + 4(0 + 1 + 2 + ... + n - 2)
The bracket being multiplied by 4 is also an arithmetic series, it will follow the arithmetic equation (n / 2)(a + l) where l is the last term, in this case n - 2
An = -1 + 7n - 7 + (4(n -1) / 2)(n - 2)
An = -1 + 7n - 7 + (2n - 2)(n - 2)
An = -1 + 7n - 7 + 2n² - 4n - 2n + 4
An = 2n² + n - 4

That's our equation to get the nth term,
An = 2n² + n - 4
Lets see if it works, for the first term n = 1
A1 = 2(1)² + 1 - 4
A1 = -1
seems to work, what about the 5th term or 51
A5 = 2(5)² + 5 - 4
A5 = 50 + 1
A5 = 51
Lastly, the 6th term as predicted by the formula should be...
A6 = 74

This was actually doing it a stranger way, where n = T where T is the term, usually T = n + 1
If T = n + 1 then the formula would be...
An = 2n² + 5n - 1
That is, this equation works where if you accept that for the first term n = 0 (rather than n = 1) and the second term n = 1 (rather than n = 2).

For fun, the 10,000th term (where T = n) should be 200,009,999.
Finding the pattern was easy, getting the general term was a bit more strange but it was fun! Give me MOAR!

[MrRazot]

0
lol you're too good for me

[anoni]

1.
I came up with a very interesting sequence
2 + 6 + 14 + 40 + 62 + ...
Finding the pattern is easy, getting a formula for it, not so much

[MrRazot]

0
lol boasting your pattern now?

[anoni]

1.
It's a neat pattern!
Who would of thought each term was itself a sum of a geometric progression

[White Wolf Guardian]

2

Well call me your sister, thats a maths!

[anoni]

3.
Hey sis!

[White Wolf Guardian]

4

*Hits with purse* I told you not to call me that! *Anime wailing of tiny arms side-to-side appearance*

[anoni]

5.
Combo...
...I don't think any members are online

[White Wolf Guardian]

6

So what :v *Party rock in the house tonight*

[anoni]

7.
I bet we could beat the record if we post fast enough

[White Wolf Guardian]

8

That I doubt considering how long it takes me to post from a cellphone. AND I'm going to sleep again

[anoni]

9.
Ok then
NEXT TIME!

When we got the record in members vs. Staff, we were posting so fast that you'd post, then as soon as you posted you'd go back to posting and two posts would have already been made

[White Wolf Guardian]

10

If I was in front of my computer, we'd already be at mid-20s probably.

[anoni]

11.
Yeah, Damn you and your mobile technology