Question

Is the sequence geometric? If so, identify the common ratio.256, 64, 16, 4…a) yes, 4b) yes, 3/4c) yes, 1/4d) no

Answer 1

Yes;
`\frac{1}4}`

Explanation:

Divide the second term by the first term, then the third term by the second term, and so on.

`(64)/(256) = 0.25, or (1)/(4) \\(4)/(16) = 0.25, or (1)/(4) \\\\(64)/(256) = 0.25, or (1)/(4) \\`

The common ratio is
`(1)/(4)`.

Answer 2

A geometric sequence is given by:

`a_n=a\cdot r^(n-1)`

Where:

a = First term of the sequence

r = Common ratio

Using the data provided:

`\begin{gathered} a=256 \\ a_2=64=256\cdot r \\ r=(1)/(4) \end{gathered}`

Therefore, the geometric sequence is:

`\begin{gathered} a_n=256((1)/(4))^(n-1) \\ _{\text{ }}since \\ a_3=16 \end{gathered}`

We can conclude it is a geometric sequence and its common ratio is 1/4

Answer:

c) yes, 1/4