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nlexa [21]
3 years ago
8

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

Mathematics
2 answers:
Olin [163]3 years ago
8 0
2nd one: an = 4(1/5)^n - 1
Sunny_sXe [5.5K]3 years ago
7 0

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}

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