Question

For the following exercise determine whether the graph shown represents a geometric sequence.

Answer 1

Answer:

Graph of a geometric sequence

equal changes in the input cause the output to be successively multiplied by a constant. cause the output to be successively multiplied by a constant (determined by the common ratio). Thus, geometric sequences always graph as points along the graph of an exponential function.

An example of a geometric sequence is given below as

A geometric sequence takes the function given in the formula below

$a_n=ar^{n-1}$

When n=1, An=-3

$\begin{gathered} a_{n}=ar^{n-1} \\ -3=ar^{1-1} \\ -3=a \\ a=-3 \end{gathered}$

When n=2 ,An=-1

$\begin{gathered} a_{n}=ar^{n-1} \\ -1=-3r^{2-1} \\ -1=-3r \\ r=\frac{-1}{-3} \\ r=\frac{1}{3} \end{gathered}$

When n=3,An =1

$\begin{gathered} a_{n}=ar^{n-1} \\ 1=3r^{3-1} \\ \frac{1}{3}=r^2 \\ r^=\sqrt{\frac{1}{3}} \end{gathered}$

We can see that they do not have a constant value of the common ratio (r)

Hence,

The graph DOES NOT represent a geometric sequence