Question

Which sequence is modeled by the graph below? coordinate plane showing the points 1, 4; 2, 0.8; and 3, 0.16

Answer 1

2nd one: an = 4(1/5)^n - 1

Answer 2

Answer:

Option 2nd is correct

$a_n = 4 \cdot (\frac{1}{5})^{n-1}$

Step-by-step explanation:

The nth term for the geometric sequence is given by:

$a_n = a_1 \cdot r^{n-1}$             ....[1]

where,

$a_1$ is the first term

r is the common ratio term

n is the number of terms.

As per the statement:

Given the coordinates points:

(1, 4), (2, 0.8) and (3, 0.16)

We can write this as:

n                   $a_n$

1`                    4

2                   0.8

3                   0.16

This is a geometric series

Here, $a_1 = 4$ and common ratio(r) = $\frac{1}{5}$

Since,

$\frac{0.8}{4} = 0.2 = \frac{1}{5}$

$\frac{0.16}{0.8} = 0.2 = \frac{1}{5}$

Substitute the given values in [1] we have;

$a_n = 4 \cdot (\frac{1}{5})^{n-1}$

Therefore, the sequence is modeled by the given graph is:

$a_n = 4 \cdot (\frac{1}{5})^{n-1}$