Question

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

an = 4(−5)n − 1
an = 4(one fifth)n − 1
an = 0.4(5)n − 1
an = one fifth(4)n − 1

Answer 1

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

Answer 2

Option 2nd is correct

`a_n = 4 \cdot ((1)/(5))^(n-1)`

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) =
`(1)/(5)`

Since,

`(0.8)/(4) = 0.2 = (1)/(5)`

`(0.16)/(0.8) = 0.2 = (1)/(5)`

Substitute the given values in [1] we have;

`a_n = 4 \cdot ((1)/(5))^(n-1)`

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

`a_n = 4 \cdot ((1)/(5))^(n-1)`