Question

For each sequence, state if it is arithmetic, geometric, or neither.{-2, 4, -8, 16, -32, 64, -128)

Answer 1

Given:

The given sequence is -2,4,-8,16,-32,64,-128

First, let's check with the ratio of the sequence.

To find the ratio,

$\begin{gathered} \frac{r_2}{r_1}=\frac{4}{-2} \\ \frac{r_2}{r_1}=-2 \end{gathered}$

Now, let's check for the next term,

$\begin{gathered} \frac{r_3}{r_2}=\frac{-8}{4} \\ \frac{r_3}{r_2}=-2 \end{gathered}$

Thus both the ratios are same.

Hence the given sequence is a geometric progression.