Question

Please help me on number 7

Answer 1

So, here we have the following sequence:

`3,(3)/(4),(3)/(16),(3)/(64),\ldots`

We want to know if this sequence can be a geometric sequence or not.

For this, we could rewrite this sequence as:

`\begin{gathered} (3)/(4^0),(3)/(4^1),(3)/(4^2),(3)/(4^3),\ldots \\ \to3\cdot(\frac{1}{4^{}})^0,3\cdot(\frac{1}{4^{}})^1,3\cdot((1)/(4))^2,3\cdot((1)/(4))^3,\ldots \end{gathered}`

As you can see, this is actually a geometric sequence, whose ratio is 1/4.