Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues.
{3, −1, 3, −1, 3, −1, ...}

Question

Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues.
{3, −1, 3, −1, 3, −1, ...}

fanduekisses · Answer

like I know for sure, it will include (-1)^n+1  times 3 raised to something

fanduekisses · Answer

the power of three must alternate between 0 and 1...

fanduekisses · Answer

hmmmm

fanduekisses · Answer

oh or (-1)^n+1 * (3+3(-1)^n+1)

fanduekisses · Answer

noo

agent0smith · Answer

Maybe you can "center it" at 1, and find a way to alternate adding and subtracting 2

fanduekisses · Answer

+2*(-1)^n+1

agent0smith · Answer

$$\large 1+2*(-1)^{n+1}$$starting with n=1

fanduekisses · Answer

yay! :)

agent0smith · Answer

Yeah your initial attempt is what gave me the idea :)

fanduekisses · Answer

thanks! ^_^

agent0smith · Answer

Since your initial attempt would alternate between 0 and 6, i just translated it

fanduekisses · Answer

yeah it makes a lot of sense :)

agent0smith · Answer

You could apply that to any sequence of that form

{a, -b, a, -b...}

$$\frac{ a-b }{ 2 }+(a-b)*(-1)^{n+1}$$

agent0smith · Answer

Wait that prob isn't right. Meh, close enough

fanduekisses · Answer

It helps though, it looks like any sequence that alternates between two numbers will include something like that

agent0smith · Answer

Yeah, it's the midpoint of the two numbers, plus the distance from the midpoint times the (-1)^n+1