Answer:
Option 2nd is correct
[tex]a_n = 4 \cdot (\frac{1}{5})^{n-1}[/tex]
Step-by-step explanation:
The nth term for the geometric sequence is given by:
[tex]a_n = a_1 \cdot r^{n-1}[/tex] ....[1]
where,
[tex]a_1[/tex] 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 [tex]a_n[/tex]
1` 4
2 0.8
3 0.16
This is a geometric series
Here, [tex]a_1 = 4[/tex] and common ratio(r) = [tex]\frac{1}{5}[/tex]
Since,
[tex]\frac{0.8}{4} = 0.2 = \frac{1}{5}[/tex]
[tex]\frac{0.16}{0.8} = 0.2 = \frac{1}{5}[/tex]
Substitute the given values in [1] we have;
[tex]a_n = 4 \cdot (\frac{1}{5})^{n-1}[/tex]
Therefore, the sequence is modeled by the given graph is:
[tex]a_n = 4 \cdot (\frac{1}{5})^{n-1}[/tex]
