Question

640, 160, 40, 10, ...

Which correctly describe the graph of the geometric sequence? Check all that apply.

The graph will show exponential growth.


The graph will appear linear.


The domain will be the set of natural numbers.

The range will be the set of natural numbers.

The graph will show exponential decay.

Answer 1

The options that hold true are:

• The domain will be the set of natural numbers.

• The graph will show exponential decay.

Explanation:

We are given a geometric sequence as:

640, 160, 40, 10, ...

Clearly we see that each term is decreasing at a constant rate as compared to it's preceding term.

Hence, the graph formed by this sequence will be a exponential graph with decay .

( since, the terms of the sequence are decreasing)

The sequence could be modeled as:

Let
`a_n` represents the nth term of the sequence.

Hence,

`a_n=640\cdot (1)/(4^(n-1))`

As, the sequence is geometric hence the domain will be a set of natural numbers.

but the range will be positive real numbers.

Hence, the correct option is:

The domain will be the set of natural numbers.

The graph will show exponential decay

Answer 2

Option 3 and 5 are correct

Explanation:

We have given a geometric series 640,160,40,10....

Common ratio of geometric series is
`r=(a_2)/(a_1)`

`r=(160)/(640)=(1)/(4)<0`

Here our common ratio is less than zero

It will show the graph of exponential decay

Hence, option 5 is correct.

The general term of geometric series is
`a_n=a\cdotr^(n-1)`

Domain will be all natural numbers since, geometric series take only natural numbers.

Here, values of "n" is domain

Hence, option 3 is correct.

Range can be any positive real numbers not only natural number

Range is the value of
`a_n`

Hence, option 4 is discarded.

Graph can not be linear of a geometric series being exponential

Hence, option 2 is discarded.

Option 1 is discarded because it is exponential decay function so it can not be exponential growth.

Therefore, Option 3 and 5 are correct.