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} (r_2)/(r_1)=(4)/(-2) \\ (r_2)/(r_1)=-2 \end{gathered}`

Now, let's check for the next term,

`\begin{gathered} (r_3)/(r_2)=(-8)/(4) \\ (r_3)/(r_2)=-2 \end{gathered}`

Thus both the ratios are same.

Hence the given sequence is a geometric progression.