Question

Which function can be used to represent the graphed geometric sequence? f(x) = 80(One-fourth) Superscript x minus 1 f(x) = 320(One-fourth) Superscript x minus 1 f(x) = 80(4)x – 1 f(x) = 320(4)x – 1.

Answer 1

You can use the formula for getting the xth term of a geometric sequence for the graphed points.

The function that represents the graphed geometric sequence is given by

Option A:  $f(x) = 80 \times (\dfrac{1}{4})^{x-1}$

What is  a geometric sequence and how to find its xth terms?

There are three parameters which differentiate between which geometric sequence we're taking about.

• The first parameter is the initial value of the sequence.
• The second parameter is the quantity by which we multiply previous term to get the next term.
• The third parameter is the length of the sequence. It can be finite or infinite.

Suppose the initial term of a geometric sequence is  $a$ and the term by which we multiply the previous term to get the next term is  $r$

Then the sequence would look like

$a, ar, ar^2 , ar^3 ....$

(till the terms to which it is defined)

Thus, the xth term of such sequence would be

$f(x) = \text{xth term} = ar^{x-1}$

How to find the function representing the graphed geometric sequence?

The points plotted in the graph are

(1,80), (2, 20), (3, 5)

The x coordinate shows the position of the term and the y coordinate shows the value of that position's term in the sequence.

So we have the sequence as

$80, 20, 5 ...$

Thus, a = 80

and we have

$r = \dfrac{ar}{a} = \dfrac{20}{80} = \dfrac{1}{4}$

Thus, the multiplication factor for the given sequence is r = 1/4

Thus, by using the xth term formula, we have:

$f(x) = \text{xth term} = ar^{x-1} = 80 \times (\dfrac{1}{4})^{x-1}\\\\f(x) = 80 \times (\dfrac{1}{4})^{x-1}$

Thus,

The function that represents the graphed geometric sequence is given by

Option A:  $f(x) = 80 \times (\dfrac{1}{4})^{x-1}$

Learn more about geometric sequence here:

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