Question

Sequence formula for {3,7,3,7..}

Answer 1

Find a general formula for this set.

Answer 2

you have the odd terms are constantly 3
and the even terms are constantly 7
set up a piecewise function saying exactly that

Answer 3

I don't think they will allow piecewise functions on my homework.

Answer 4

Or is there any other way to figure this out??

Answer 5

well I suppose we can write it another way
so we have (-1)^n=1 if n is odd and -1 if n is even
I think we can use this to get our 3 and out 7
for example pretend we have
5,9,5,9,...
so we can do this
\[a_n=\frac{9+5}{2}+\frac{9-5}{2}(-1)^n \\ a_n=7+2(-1)^n \]

Answer 6

Wow, that is VERY smart

Answer 7

I think that will always work for sequences like this
a,b,a,b,...
assume b>a
\[A_n=\frac{b+a}{2}+\frac{b-a}{2}(-1)^n\]

Answer 8

I called the sequence big A so not confuse with the little number a in that sequence
(remember math is case sensitive) :)

Answer 9

but

Answer 10

OH never mind (: Thank you

Answer 11

Is this a formula I should memorize?