# Question #eab17

Aug 23, 2017

General formula for the nth term is ${a}_{n} = 4 \cdot {\left(- \frac{1}{2}\right)}^{n}$

The first 7 terms are:

$4 , - 2 , 1 , - \left(\frac{1}{2}\right) , \frac{1}{4} , - \left(\frac{1}{8}\right) , \frac{1}{16}$

#### Explanation:

This is a geometric sequence. We start with ${a}_{0} = 4$, progress to ${a}_{1} = - 2$ and so on.

Notice that if you divide a term by the previous term,you will always get the same value. This is the common ratio of the sequence.

$r = {a}_{1} / {a}_{0} = \frac{- 2}{4} = - \frac{1}{2}$

To progress from one term to the next, we simply multiply by r. This means that to get to the nth term of the sequence from the first term, we multiply by r and we do it n times (ie multiply by ${r}^{n}$).

Therefore ${a}_{n} = {a}_{0} \cdot {r}^{n} = 4 \cdot {\left(- \frac{1}{2}\right)}^{n}$