[Coda]

Originally Posted by Potironette

I thought the pointing end was the compass's north pole..?

Nope, because opposite poles attract. It's the part of the compass LABELED north, but magnetically speaking it's the south pole.

Oops, I forgot ._.'''. So basically I can find the sum at any position (n) with closed form and that's what closed form is?

Yup.

So to find a ratio I just look at one value and the next and if I don't know how much to multiply the first by, I just divide the next from the previous!

Yup.

Although, wouldn't that be 5^c?

Um...

5^nc+1 / 5^(n-1)c+1
5^{(nc+1) - ((n-1)c+1)}
5^{nc + 1 + -(nc + -c + 1)}
5^{nc + 1 + -nc + c + -1}
5^{nc + -nc + 1 + -1 + c}
5^c

... yep, you're right, my mistake!

I messed up writing it, woops. a = a₁. And 'a' represents the first term in an arithmetic series. d is the difference between two terms in an arithmetic series. S_n in this case is the sum for the arithmetic series. I learned to use those formulas to find the sum of things such as 1, 3, 5, ... up to a specified nth term in class.

That means that d = a₂ - a₁, so you can substitute that into the expression.

n(2a₁ + (n-1)d)/2 = n((a₁+a₂)/2)
n(2a₁ + (n-1)(a₂ - a₁))/2 = n((a₁+a₂)/2)
2a₁ + (n-1)(a₂ - a₁) = a₁+a₂
2a₁ + (n-1)a₂ - (n-1)a₁ = a₁+a₂
2a₁ - (n-1)a₁ + (n-1)a₂ = a₁+a₂
(2 - n - 1)a₁ + (n-1)a₂ = a₁+a₂
(1 - n)a₁ + (n - 1)a₂ = a₁+a₂
(n - 1)(a₂ - a₁) = a₁+a₂

... by all accounts it doesn't make sense. Did I make a mistake, or did you transcribe something else wrong?