Discovering the Formula for a Repeating Sequence

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I have to find a formula for the general term of An for this sequence assuming that the pattern follows and continues. (13,3,13,3...)
I don't think there's any straightforward formulas to use for sequences and series' in finding a formula.
My attempt involved finding two numbers that add to 13 and subtract to 3 which is 8 and 5, but what I'm stuck on is inserting the n variable so that the pattern will keep repeating 13,3,13,3..so on. Totally lost on how to do it and it doesn't even seem that hard.
 
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Try A_n = 8 + 5*(-1)^(n+1).
 
figured it out thanks for the tip
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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