# explicit formula for alternating sequence

find an explict formula for the sequence of the form $$a_1,a_2,a_3,...$$ with the initial terms $$\frac{1}{5},\frac{-2}{7},\frac{4}{9},\frac{-8}{11},\frac{16}{13},...$$

$$a_n = \frac{2^n(-1)^n}{5+2^n}$$

this seems to work if I can start with $$a_0$$

but It seems it cannot work this way? What is the correct formula for this sequence and do I have to start at $$a_1$$

• Actually it doesn't work if you start from $a_0$ check the value for $a_3$. May 12 '15 at 1:09

Try $$a_n=-\frac{(-1)^n2^{n-1}}{2n+3}$$