What is explicit formula for each term in the sequence such that the pattern is as follows:
{5,1,5,1,5,1,5,1...}?

No idea how to do this...I tried {5^n/5^(1-n)} obviously doesn't work. I think it is something like this so it differs from odd to even terms...but I can't figure it out.

Question

What is explicit formula for each term in the sequence such that the pattern is as follows:
{5,1,5,1,5,1,5,1...}?

No idea how to do this...I tried {5^n/5^(1-n)} obviously doesn't work. I think it is something like this so it differs from odd to even terms...but I can't figure it out.

zarkon · Answer

$$a_{n}=\alpha+(-1)^{n}\beta$$

$$a_0=\alpha+(-1)^0\beta=5\Rightarrow \alpha+\beta=5$$
$$a_1=\alpha+(-1)^1\beta=5\Rightarrow \alpha-\beta=1$$

add the two equations

then $$2\alpha=6\Rightarrow \alpha=3$$

then $$3-\beta=1\Rightarrow \beta=2$$

so 

$$a_{n}=3+(-1)^n\cdot 2,\,\,\,n=0,1,2\ldots$$

anonymous · Answer

how do you know to use a(k) = alpha + (-1)^k * beta?

zarkon · Answer

because the sequence is just repeating two numbers