# How do you write the first five terms of the sequence a_n=(-1/2)^n?

May 25, 2018

Plug it in!

#### Explanation:

So we have to know where the sequence starts, but we will assume it starts at $n = 0$ (there may be some different practice in your class, usually $n = 1$ if not $n = 0$)

Therefore, we can plug in the first few:
${a}_{0} = {\left(- \frac{1}{2}\right)}^{0} = 1$
${a}_{1} = {\left(- \frac{1}{2}\right)}^{1} = - \frac{1}{2}$
${a}_{2} = {\left(- \frac{1}{2}\right)}^{2} = \frac{1}{4}$
${a}_{3} = {\left(- \frac{1}{2}\right)}^{3} = - \frac{1}{8}$
${a}_{4} = {\left(- \frac{1}{2}\right)}^{4} = \frac{1}{16}$

giving us the beginning of our sequence.